Unit 1

1. Atomic Structure and Periodicity

The development of modern atomic theory revealed much about the inner structure of
atoms. It was learned that an atom contains a very small nucleus composed of positively
charged protons and uncharged neutrons, surrounded by a much larger volume of space
containing negatively charged electrons. The nucleus contains the majority of an atom’s
mass because protons and neutrons are much heavier than electrons, whereas electrons
occupy almost all of an atom’s volume. The diameter of an atom is on the order of 10−10
m, whereas the diameter of the nucleus is roughly 10−15 m, about 100,000 times smaller.

In order to understand the structure of an atom, different types of atomic models were
developed using different instruments. Some of the models are:
1.1. Democritus theory (300 BC)
The Greek philosopher Democritus expressed his own postulate and he states that:
Matter consists of very small, indivisible particles which are called as atoms. Atoms are
derived from Greek words ATOMOS which mean indivisible into smaller particle.
Atoms are indivisible particles. Explains certain natural occurrences such as the existence
of elements
Atoms-and the protons, neutrons, and electrons that compose them—are extremely small.
Atomic theory describes about the historical models of the atom, especially the external
structure of atoms and how atoms combine to form molecules. This theory is a scientific
theory that deals the nature of matter; states that matter is composed of discrete units
which called atoms. Atom is the smallest particle into which an element can be divided
and still be the same substance. Atoms are so small until recently, no one had ever seen it.
But ideas, or theories, about atoms have been around for over 2,000 years. The theory of
the atom has had a long history. The ancient Greeks postulated that matter exists in the
 form of atoms. But they did not base their theory on experiment and they cannot develop
additional ideas about atoms. Different scholars (researchers) give their idea on the
atomic theory.
Limitation of Democritus atomic theory
 His theory does not support by experiment but only theoretical view
 Does not have any information about subatomic particles (electron, proton and
neutron). Due to the lack of experiment, Democritus’ idea was not accepted by many
of researchers or scholars because Experimental evidence from early scientific
investigations provided support for the notion of “atomism” and gradually gave rise to
the modern definitions of elements and compounds.
1.2. Dalton’s Atomic Theory
John Dalton (1766-1844), an English schoolteacher, developed the first useful atomic
theory of matter around 1808. His findings were based on experiments and also from
laws of chemical combination. He used fundamental laws of chemical combination just
described as the basis of an atomic theory. His theory involved many assumptions:
 All substances are composed of tiny, indivisible particles which called “atoms”.
 Atoms of the same element are identical in size, mass and properties but, atoms of
different elements have different properties (he doesn’t recognize isotopes).
 Compounds are formed by the union of two or more different elements
 Dalton model is known as the solid sphere model (like billiard balls)
Importance and Improvement on previous model
 Explains how atoms combine to form molecules.
 Explains chemical change better than the particle theory.
 Define conservation of mass and definite proportion.
Dalton’s theory put down a corner stone for modern atomic theories since he uses the
law of chemical combination.
1.2.1. Laws of Chemical Combination
Various chemical reactions take place according to certain laws, known as the Laws of
chemical combination. There are three common laws of chemical combinations. These
are:
A. Law of conservation of mass/the law of mass action: It also known as the law of
indestructibility of matter since this law states that “matter is neither created nor
destroyed in the course of chemical reaction rather it may change from one form to
other”. The total mass of materials after a chemical reaction is same as the total mass
before reaction. In short this law states that “during any physical or chemical changes, the
total mass of product equal to the total mass of reactants”. For example, in an experiment
63.5g of copper combines with 16g of oxygen to give 79.5g of cupric oxide (a black
oxide of copper).

2Na + Cl2 →2NaCl,

2x23+2x35.5=117=2(23+35.5)=117
B. Law of constant or definite composition: According to this law, in a given
compound, the constituent elements are always combined in the same proportions by
mass, regardless of the origin or mode of preparation of the compound. What this law
means is that when elements react chemically, they combine in specific proportions, not
in random proportions. A sample of pure water which obtains river, sea, well, spring
whatever the source, always contains 88.9% by mass of oxygen and 11.1% by mass of
hydrogen.

C. Law of multiple proportions: According to this law, when two elements A and B
combine to form more than one chemical compounds then different weights of A, which
combine with a fixed weight of B, are in proportion of simple whole numbers. Or when
two/more elements combine to form two/more compounds, the mass of one element
combines with a fixed mass of another element. Example: Carbon monoxide (CO): 12
parts by mass of carbon combines with 16 parts by mass of oxygen. Carbon dioxide
(CO2): 12 parts by mass of carbon combines with 32 parts by mass of oxygen. Ratio of
the masses of oxygen that combines with a fixed mass of carbon (12 parts) is 16: 32 or 1:
2

Limitations of Dalton’s atomic theory

 Does not include the existence of the nucleus
 Does not explain the existence of ions or isotopes
  Does not have any information on subatomic particles (electron, proton and
neutron).

Example 1. A nitrogen-oxygen compound is found to have an oxygen-to-nitrogen mass

ratio of 1.142 g oxygen for every 1.000 g of nitrogen. Which of the following oxygen-to-
nitrogen mass ratio(s) is/are possible for different nitrogen-oxygen compound(s)? a 2.285
c 0.571 b 1.000 d 2.500 2. Determine, which of the following oxygen-to-nitrogen mass
ratio(s) is/are also possible for nitrogen-oxygen compound. (Refer Example 2.1 No. 1 for
required information) a 0.612 c 1.713 b 1.250 d 2.856

Solution: 1. The given compound has 1.142 g of oxygen and 1.000 g of nitrogen.
Response (a) has 2.285 g of oxygen for the same 1.000 g of nitrogen. The ratio of the
masses of oxygen, 2.285:1.142, is almost exactly 2:1. Response (a) seems to be correct
possibility, so is response (c). Here the ratio is 0.571:1.142 = 0.500 = 1:2. Responses (b)
and (d) are not possibilities. They yield ratios of 1.000:1.142 = 0.875 and 2.500: 1.142 =
2.189, respectively. Neither of these can be expressed as a ratio of small whole numbers.
2. By the same method, a 0.612:1.142 = 0.536:1 is not possible b 1.250:1.142 = 1.095:1
is not possible c 1.713:1.142 = 1.5:1 or 3:2, is possible d 2.856:1.142 = 2.5:1 or 5:2 is
possible

Exercise 1

1. List the postulates of Dalton that continue to have significance (are retained in modern
atomic theory). 2. Match the atomic theory statements in part A with the matching items
in part B.
1.3. The concept of the atom
2.3.1. Discoveries of subatomic particles

Name location Charge(C) Unit Mass(amu) Mass(g) Discovered by

charge

Electron Outside −1.602× 10−19 -1 0.00055 0.00091 × 10−24 Joseph John

nucleus Thomson

Proton Nucleus 1.602 ×10−19 +1 1.00727 1.67262 × 10−24

Neutron Nucleus 0 0 1.00866 1.67493 × 10−24 James

Chadwick

A. Cathode Rays

In 1879, the English scientist William Crookes (1832-1919) experimented with gas
discharge tubes. When a very high electrical potential (~ 10,000 volts) is applied across a
gas taken in a discharge tube of a very low pressure (~ 0.001 torr) some radiations are
emitted from cathode. These radiations are called cathode rays. Fig 2.1, shows emission
of cathode rays in a discharge tube. At this stage the glass walls of the discharge tube
opposite to the cathode starts glowing with a faint greenish light. It is now known that
this greenish glow on the walls is due to the bombardment of the glass wall with the
cathode rays.

Cathode rays normally travel in straight lines, but are deflected when a magnet is brought
nearby (Figure 2.1b).

Figure 1 (a) Electric discharge in an evacuated tube (b) The cathode ray is bent. in the presence of a
magnet.
An English physicist Joseph John Thomson (1856-1940) in 1897 studied the behaviour of
cathode rays in electric and magnetic fields, Thomson established clearly that the rays
consist of negatively-charged particles. Moreover, his experiments showed that the
particles were identical, regardless of the materials from which the belectrodes were
made or the type of gas in the tube. Thomson concluded that these negatively charged
particles were constituents of every kind of atom. We now call these particles electrons, a
term that had been coined by the Irish Physicist George Stoney in 1891 to describe the
smallest unit of electric charge. Cathode rays are beams of electrons. In 1909, Robert A.
Millikan, an American physicist, determined the charge on the electron by observing the
behaviour of electrically-charged oil drops in an electric field. Based on careful
experiments, Millikan established the charge on an electron as e = –1.602 × 10–19 C.
From this value and the value for me /e, we can calculate the mass of an electron.

B. Radioactivity and Discovery of Nucleus

I. Radioactivity
Radioactivity is the spontaneous emission of radiation from the unstable nuclei of certain
isotopes. Isotopes that are radioactive are called radioactive isotopes or radioisotopes. For
example,

are radioactive isotopes. Radioactive decay is defined as a nuclear breakdown in which

particles or (electromagnetic) radiation is emitted. Shortly after the discovery of
radioactivity, three types of rays were identified in the emanations from radioactive
substances. One type called alpha (α) particles which consist of particles that have a mass
that is about four times that of a hydrogen atom. They also have a charge twice the
magnitude of an electron but positive rather than negative. An alpha particle is now
known to be a doubly-ionized helium atom, that is, He2+.
A second type of radiation was shown to consist of negatively-charged particles, identical
to cathode rays. These particles are called beta (β) particles, which are electrons, coming
from inside the nucleus.
The third type of radiation, called gamma (γ) rays, is a form of electromagnetic radiation
much like the X-rays but of even higher energy. Like X-rays, but unlike alpha and beta
particles, gamma rays are a form of energy and not a form of matter.
II. Discovery of Nucleus
In 1910, the New Zealand chemist and physicist, Ernest Rutherford, who had studied
with J.J. Thomson decided to use α-particles to probe the structure of atoms.
Together with his associate Hans Geiger, Rutherford carried out a series of experiments
using very thin foils of gold and other metals as targets for α-particles from a radioactive
source.

Figure 2. a. Rutherford’s experimental design for measuring the scattering of α-particles by a piece of gold
foil. b. Magnified view of α-particles passing through and being deflected by the nucleus.

C. Discovery of Neutron
Except for the lightest hydrogen isotope, protium (1H), atoms have more mass than is
indicated by the numbers of their protons (Before the 1930’s, protons were considered as
the sole contributors to the mass of an atom). For example, a helium nucleus, with two
protons has a mass four times that of hydrogen. If all the mass came from the protons, a
helium atom would have only twice the mass of a hydrogen atom. The reason for this
“excess” mass puzzled scientist for several years.
In the 1920s and early 1930s, alpha particles were used as projectiles to bombard a
variety of materials. Bombardment of beryllium atoms produced a strange, highly
penetrating form of radiation. In 1932, James Chadwick (1891-1972) showed that this
radiation was best explained as a beam of neutral particles. These particles, called
neutrons, were found to have about the same mass as protons but no electric charge.
This discovery finally provided an explanation for the mysterious excess mass. A helium
atom has two protons and two neutrons. Because protons and neutrons have roughly the
same mass (and electrons have almost no mass) the helium atom should have about four
times the mass of the hydrogen atom. The mass of a neutron, mn = 1.67493 × 10–27 kg, is
about 1840 times the mass of electron.
1.4. Atomic Mass and Isotopes

The number of protons in the nucleus of an atom is its atomic number (Z). This is the
defining trait of an element: Its value determines the identity of the atom. For example,
any atom that contains six protons is the element carbon and has the atomic number 6,
regardless of how many neutrons or electrons it may have. A neutral atom must contain
the same number of positive and negative charges, so the number of protons equals the
number of electrons. Therefore, the atomic number also indicates the number of electrons
in an atom. The total number of protons and neutrons in an atom is called its mass
number (A). The number of neutrons is therefore the difference between the mass number
and the atomic number: A – Z = number of neutrons.

Atoms are electrically neutral if they contain the same number of positively charged
protons and negatively charged electrons. When the numbers of these subatomic particles
are not equal, the atom is electrically charged and is called an ion. The charge of an atom
is defined as follows:

Atomic charge = number of protons − number of electrons

As will be discussed in more detail later in this chapter, atoms (and molecules) typically
acquire charge by gaining or losing electrons. An atom that gains one or more electrons
will exhibit a negative charge and is called an anion. Positively charged atoms called
cations are formed when an atom loses one or more electrons. For example, a neutral
sodium atom (Z = 11) has 11 electrons. If this atom loses one electron, it will become a
cation with a 1+ charge (11 − 10 = 1+).

A neutral oxygen atom (Z = 8) has eight electrons, and if it gains two electrons it will
become an anion with a 2- charge (8 − 10 = 2-).
Atomic mass unit and average atomic mass because each proton and each neutron
contribute approximately one amu to the mass of an atom, and each electron contributes
far less, the atomic mass of a single atom is approximately equal to its mass number (a
whole number). However, the average masses of atoms of most elements are not whole
numbers because most elements exist naturally as mixtures of two or more isotopes.

The mass of an element shown in a periodic table or listed in a table of atomic masses is a
weighted, average mass of all the isotopes present in a naturally occurring sample of that
element. This is equal to the sum of each individual isotope’s mass multiplied by its
fractional abundance.

For example, the element boron is composed of two isotopes: About 19.9% of all boron
atoms are 10B with a mass of 10.0129 amu, and the remaining 80.1% are 11B with a
mass of 11.0093 amu. The average atomic mass for boron is calculated to be:
Calculation of Average Atomic Mass: A meteorite found in central Indiana contains
traces of the noble gas neon picked up from the solar wind during the meteorite’s trip
through the solar system. Analysis of a sample of the gas showed that it consisted of
91.84% 20Ne (mass 19.9924 amu), 0.47% 21Ne (mass 20.9940 amu), and 7.69% 22Ne
(mass 21.9914 amu). What is the average mass of the neon in the solar wind?

Exercise 2. There are two isotopes of lithium found on earth. Isotope 6Li (6.01512 mu)
accounts for 7.42% of the total, and isotope 7Li (7.01600 mu) accounts for the remaining
92.58%. What is the average atomic mass of lithium?

Solution:

2. What is the mass number of an isotope of tin that has 66 neutrons and 50 protons?
3. Calculate the number of protons and neutrons for 24 12Mg and 88 38Sr.
4. Why do isotopes of an element have similar chemical properties?
5. Element X is toxic to humans in high concentration but essential to life at low
concentrations. Identify element X whose atoms contain 24 protons and write the symbol
for the isotope with 28 neutrons
6. Copper (Cu: atomic mass 63.546 mu) contains the isotopes 63Cu (mass = 62.9298 mu)
and 65Cu (mass = 64.9278 mu). What percent of a Cu atom is 65Cu?
7. The element chlorine contains two isotopes: 35Cl, which has a mass of 34.97 mu, and
37
Cl, which has a mass of 36.97 mu. Calculate the percentage of each chlorine isotope.
The average atomic mass of chlorine is 35.5 mu.
8. Carbon exists as the isotopes carbon-12, with a fractional abundance of 0.9890 and a
mass of exactly 12 mu, and carbon-13, with a fractional abundance of 0.0110 and a mass
of 13.00335 mu. Calculate the average atomic mass of carbon
1.5. The Bohr Theory of the hydrogen atom

In 1913, Niels Bohr, a Danish physicist, who had worked with Rutherford, combined
ideas from classical physics and the new quantum theory to explain the structure of the
hydrogen atom. He suggested a model for the hydrogen atom that predicted the existence
of line spectra. In doing so, he was able to explain the spectrum of radiation emitted by
hydrogen atoms in gas-discharge tubes.

Based on the work of Planck and Einstein, Bohr made the revolutionary assumption that
certain properties of the electron in a hydrogen atom – including energy, can have only
certain specific values. That is to say, these properties are quantized. Bohr proposed the
following three postulates for his model.

1. The hydrogen atom has only certain allowable energy levels, called stationary states.
Each of these states is associated with a fixed circular orbit of the electron around the
nucleus.
2. The atom does not radiate energy while in one of its stationary states. That is, even
though it violates the ideas of classical physics, the atom does not change energy while
the electron moves within an orbit.
The electron moves to another stationary state (orbit) only by absorbing or emitting a
photon whose energy equals the difference in the energy between the two states.

The subscripts f and i represent the final and the initial states, respectively. The Bohr
radius, denoted by ao (ao = 0.0529 nm) can be calculated using the formula

where n is a positive integer which is called quantum number. r is the radius of the orbit
and is given by:

where εo is the vacuum dielectric constant (εo = 8.854 × 10–12 C V–1 m–1).

A spectral line results from the emission of a photon of specific energy (and therefore, of
specific frequency), when the electron moves from a higher energy state to a lower one.
An atomic spectrum appears as lines rather than as a continuum because the atom’s
energy has only certain discrete energy levels or states.
In Bohr’s model, the quantum number n (n = 1, 2, 3 ...) is associated with the radius of
the electron’s orbit, which is directly related to the atom’s energy. The lower the quantum
number, the smaller is the radius of the orbit and the lower is the energy level of the
atom. When the electron is in the orbit closest to the nucleus (n = 1), the atom is in its
lowest (first) energy level, which is called the ground state. By absorbing a photon whose
energy equals the difference between the first and second energy levels, the electron can
move to the next orbit. This second energy level (second stationary state) and all higher
levels are called excited states. The hydrogen atom in the second energy level (first
excited state) can return to the ground state by emitting a photon of a particular
frequency:

Where Eg and Ee represent the ground and the excited energy states, respectively. When a
sample of atomic hydrogen absorbs energy, different hydrogen atoms absorb different
amounts. Even though each atom has only one electron, so many atoms are presented that
all the allowable energy levels (orbits) are populated by electrons. When an electron
drops from orbits with n > 3 (second excited state), the infrared series of spectral lines is
produced i.e, Paschen Series. The visible series arises from the photons emitted when an
electron drops to the n = 2 orbit i.e, Balmer Series (first excited state), and the ultraviolet
series arises when these higher energy electrons drop to the n = 1 orbit (ground state).
Figure 3. Representation of the observed spectral lines of the hydrogen atom.

Since a larger orbit radius means a higher atomic energy level, the farther the electron
drops, the greater is the energy (higher v, shorter λ) of the emitted photon. The spectral
lines of hydrogen become closer and closer together in the short wavelength (high
energy) region of each series because the difference in energy associated with the jump
from initial state ( ni ) to the final state (nf ) becomes smaller and smaller as the distance
from the nucleus increases.
Having made this basic assumption, Bohr was then able to use classical physics to
calculate properties of the hydrogen atom. In particular, he derived an equation for the
electron energy (En ). Each specified energy value (E1, E2, E3...) is called an energy level
of the atom. A very useful result from Bohr’s work is an equation for calculating the
energy levels of an atom,
 –18
Where A is the constant, has a value of, A = 2.18 × 10 J. The number n is an integer
called the principal quantum number (n = 1, 2, 3, ...). Z is the charge of the nucleus. The
negative sign in the equation appears because it is defined as zero energy when the
electron is completely moved form the nucleus, i.e. En = 0 when n =, so, En < 0 for any
smaller n.
A can be expressed in terms of Rydberg constant as A = hCR , where R is Rydberg
constant with a value of 1.0967 x107M-1 . For the H atom, Z = 1, so we have

Therefore, the energy of the ground state n = 1 is –2.18 × 10–18 J. This equation is easily
adapted to find the energy difference between any two levels:

• When an electric discharge is passed through a sample of hydrogen, the H2

molecules dissociate into atoms, and the electron in a particular H atom is excited.
• These states are transient and the electron falls back to a lower energy state by
emitting energy as it does so.
• The consequence is the observation of spectral lines in the emission spectrum of
hydrogen.
• The spectrum (a small part of which is shown in below Figure consists of groups
of discrete lines.
• In1885, Balmer pointed out that the wave number of the spectral lines observed in
the visible region of the atomic spectrum of hydrogen is given by V= R ( 1/22-
1/n2)
where, R = Rydberg constant for =1.097 x 107 m-1 = 1.097 x 105 cm-1
and n is an integer 3, 4, 5 . . .
 • Wave number = reciprocal of wavelength(v=1/λ); convenient (non-SI) units are
‘reciprocal centimetres’, cm-1

Figure 4. Spectrum of hydrogen

Note that: the line become close together as the wave length decrease until the
continuum reached
Similar equation will be developed to hold for the other series in
the H- spectrum

Example 2. Calculate the wave number if an electron transit from1st energy level to 5th
energy level in Uv, visible and infrared region

Example 3. Calculate wave number for third transition in:

A. Lyman series B. Balmer series C. Paschen series D. Bracket

series

Example 4. Calculate wave length for 6th transition in Balmer series

• Solution:

• given:- ni= 1 nf= 5

i. V= R(1/12-1/n2)-----------uv region

= 1.097 x 107 m-1 (1/12-1/52)= 1.05X 107 m-1

ii. V= R(1/22-1/n2) ---------- visible region

V=1.097 x 107 m-1 (1/4-1/52) = 1.05X 107 m-1

= 0.21 X1.097 x 107 m-1 = 2.3 x 106 m-1

iii. V= R(1/32-1/n2) ---------- visible region

V=1.097 x 107 m-1 (1/9-1/52)= 1.097 x 107 m-1 x 0.071

=0.077887x 107 m-1 = 7.789x 105 m-1

1.6. The quantum mechanical model of the atom

Bohr’s model was very important because it introduced the idea of quantized energy
states for electrons in atoms. This feature is incorporated in our current model of the
atom, the quantum mechanical model of the atom.
The sophisticated mathematical description of atomic structure based on the wave
properties of subatomic particles is called wave mechanics or quantum mechanics.
Principally, the Austrian physicist Erwin Scrödinger developed a model of the hydrogen
atom based on the wave nature of the electron in the late 1920s.
Mathematical equations describing the nature of electron waves in atoms are fundamental
to the modern picture of the atom. The wave equations that are acceptable solutions to the
Schrödinger equation are called wave functions. To obtain one of these acceptable
solutions, we must assign integral values called quantum numbers to three quantities in
the wave equation. This requirement is similar to the requirement for an integral value of
n in the Bohr equation for the hydrogen atom.
In contrast to the precise planetary orbits of the Bohr atom, the wave mechanics picture
of the hydrogen atom is less certain. Instead of determining the exact location of the
electron, we can only speak of the probability of the electron being found in certain
regions of the atom. Or, if we adopt the view that the electron is just a cloud of negative
electric charge, we can only speak of the charge densities in various parts of the atom.
quantum mechanical model of the atom is called Modern Atomic Theory (Electron Cloud
Mode) It states that “electrons are always moving around the nucleus in a "cloud" of
energy levels”. It also states that the small particle atom is consists of three parts such as,
proton, neutron and electron.
 The electrons are found around the nucleus whereas; protons and neutrons are
found in the central part of atom which is called nucleus.
 Describes that, the mass of one atom is the summation of the number of proton
and the number of neutrons. A= p + n
 NB: the mass of an atom is occupying by the nucleus whereas the large space of
the atom is occupying by electrons.

1.6.1. Quantum Model of Atom

 Bohr's theory worked well for hydrogen atom (one electron).
 Complications such as elliptical rather than circular orbits were introduced in an
attempt to fit the data to Bohr’s theory.
 The Bohr Atomic Theory and its modifications that forced the theorists to work
hard to explain the spectroscopists’ observations.
 In spite of their efforts, the Bohr Atomic Theory eventually proved
unsatisfactory; the energy levels are valid only for the hydrogen atom.
 An important characteristic of the electron, its wave nature, still needed to be
considered.
 According to the de Broglie equation, proposed in the 1920s, all moving
particles have wave properties described by the equation

 where λ=wavelength of the particle, h = Planck's constant, m = mass of the

particle, v = velocity of the particle.
 Particles massive enough to be visible have very short wavelengths, too small to
be measured.
 Electrons, on the other hand, have wave properties because of their very small
mass.
  Electrons moving in circles around the nucleus (in Bohr’s Atomic theory), can be
thought of as forming standing waves that can be described by the de Broglie
equation.
 However, we no longer believe that it is possible to describe the motion of an
electron in an atom so precisely.
 This is a consequence of another fundamental principle of modern physics,

1.6.2. The Heisenberg's Principle

Heisenberg formulated what is known as the Heisenberg uncertainty principle, which
states that it is impossible to know simultaneously both the momentum and the position
of a particle with certainty. Mathematically,
 Heisenberg's uncertainty principle, which states that there is a relationship
between uncertainties in the location and momentum of an electron moving in
the x direction:

Where:
 Δx= uncertainty in the position of the electron
 Δp= uncertainty in the momentum of the electron.
 Working with Heisenberg’s Principle, Schrödinger developed a compromise which
calculates both the energy of an electron and the probability of finding an electron
at any point in the molecule.
1.6.3. Quantum Numbers
An atomic orbital is specified first by three quantum numbers that are associated
respectively, with the orbital's size (energy), shape, orientation and, later, independent of
these three quantum numbers, the electron spins. The first three sets of quantum numbers
have a hierarchical relationship: the size-related number limits the shape related number,
the shape-related number in turn limits the orientation-related number.
Three among the four quantum numbers characterize the orbitals in the atom. That is,
they describe the orbital or the space the electron is supposed to occupy. The fourth
quantum number is used to describe the spin of the electrons that occupy the orbitals.
 The four quantum numbers are:
 1. The principal quantum number (n) is a positive integer having values n = 1, 2, 3, ...
.
 It gives the following information:
 (i) Relative size of the orbital or the relative distance of the electron from the nucleus.
Size of orbital increases with the increase of principal quantum number n.
 (ii) Energy of the orbital. Higher the n value, greater is the energy. For example:
when the electron occupies an orbital with n = 1, the hydrogen
 atom is in its ground state and has lower energy than when the electron occupies an
orbital with n = 2 (first excited state).
 (iii) Maximum number of electrons present in any shell (given by the formula 2n2).
2. The azimuthal quantum number (l) is also known as angular momentum or subsidiary
quantum number. It is an integer having values from 0 to (n – 1). For an orbital with n =
1, l can have a value only of 0. For orbitals with n = 2, l can have a value of 0 or 1; for
those with n = 3, l can be 0, 1 or 2; etc. So, the number of possible l values equals the
value of n. For a given value of n, the maximum possible value of l is (n – 1). The
azimuthal quantum number gives the following information: Number of subshell present
within any shell.
(ii) It describes the shape of the orbital and is sometimes also called the orbital-shape
quantum number.
3. The magnetic quantum number (ml) is also known as the orbital-orientation quantum
number. It is an integer having values from –l through 0 to +l. The possible values of an
orbital's magnetic quantum number are set by its angular momentum quantum number
(that is, l determines ml). An orbital with l = 0 can have only ml = 0. However an orbital
with l = 1, can have ml value of –1, 0, or + 1; thus there are three possible orbitals with l
= 1 each with its own spatial orientation. The number of possible ml values or orbitals for
a given l value is (2l + 1). It prescribes the orientation of the orbital in the three-
dimensional space about the nucleus.
4. The electron spin quantum number (ms ) has only two possible values, +½
(represented by the arrow, ) and – ½ (represented by the arrow ). The name electron
spin quantum suggests that electrons have a spinning motion. However, there is no way
to attach a precise physical reality to electron spin. The quantum numbers specify the
energy states of the atom.
• The atom's energy levels or shells are given by the n value.
• The atom's sublevels or subshells are given by the n and l values. Each level contains
sublevels that designate the shape of the orbital.
• The atom's orbitals are specified by the n, l and ml values. Thus, the three quantum
numbers that describe an orbital express its size (energy), shape and spatial orientation.
Each sublevel is designated by a letter:
l = 0, is an s sublevel
l = 1, is a p sublevel
l = 2, is a d sublevel
l = 3, is a f sublevel
The letters s, p, d, and f are derived from the names of spectroscopic lines: s, sharp; p,
principal; d, diffuse; and f, fundamental. Sublevels are named by joining the n value and
the letter designation. For example, the sublevel (subshell) with n = 2, l = 0 is called the
2s sublevel; the only orbital in this sublevel has n = 2, l = 0 and ml = 0. A sublevel with n
= 3, l = 1, is a 3p sublevel. It has three possible orbitals: one with n = 3, l = 1 and ml = –1
; another with n = 3, l = 1 and ml = 0 and the third n = 3, l = 1, and ml = +1.
For a given principal quantum number, n, the total number of orbitals is determined as:
Number of orbitals = n2 in a shell.
Similarly, the number of orbitals in each subshell is determined as:
 Number of orbitals in a subshell = 2l+1.
Example 5
1. What values of the angular momentum quantum number (l) and magnetic quantum
number (ml ) are allowed for a principal quantum number (n) of 3? How many orbitals
are allowed for n = 3?
2. Give the name, magnetic quantum numbers, and numbers of orbitals for each sublevel
with the following quantum numbers:
a. n = 3, l = 2 c. n = 5, l = 1
b. n = 2, l = 0 d. n = 4, l = 3
3. What is wrong with each of the following quantum number designations and/or
sublevel names?

Exercise 2
1. Give the sublevel notation for each of the following sets of quantum numbers.
a. n = 3, l = 2 c. n = 4, l = 1
b. n = 2, l = 0 d. n = 4, l = 3
2. Indicate whether each of the following is a permissible set of quantum numbers. If the
set is not permissible, state why it is not.
a. n = 3, l = 1, ml = +2 b. n = 4, l = 3, ml = –3 c. n = 3, l = 2, ml = –2
d. n = 0, l = 0, ml = 0 e. n = 3, l = 3, ml = –3
3. Consider the electronic configuration of an atom:
a. What are the n, l and ml quantum numbers corresponding to the 3s orbital?
b. List all the possible quantum number values for an orbital in the 5f sub shell.
c. In which specific subshell will an electron be present if the quantum numbers n = 3, l =
1, and ml = –1?
4. Which of the quantum numbers relates to the electron only? Which relate (s) to the
orbital?
1.7. The electromagnetic radiation and atomic spectra

1.7.1. Electromagnetic radiation

In 1873, James Clerk Maxwell proposed that light consists of electromagnetic waves.
According to his theory, an electromagnetic wave has an electric field component and a
magnetic field component. Further, his theory accurately describes how energy, in the
form of radiation, propagates through space as electric and magnetic fields.
Electromagnetic radiation is the emission and transmission of energy in the form of
electromagnetic waves. The wave properties of electromagnetic radiation are described
by two interdependent variables, frequency and wavelength. Wavelength (λ, Greek
lambda) is the distance between any point on a wave and the corresponding point on the
next wave; that is, the distance the wave travels during one cycle.

Figure 5. Electromagnetic wave

In Figure 5, two waves with different wave lengths (λ) and thus different frequencies (ν)
are shown. Wavelength is commonly expressed in meters, but since chemists often deal
with very short wavelengths the nanometre, picometer and the angstrom are also used.
Frequency (ν Greek nu) is the number of cycles that pass a given point in space per
second, expressed in units of s–1 or hertz (Hz). The speed of the electromagnetic wave
(light), c (distance travelled per unit time, in meters per second), is the product of its
frequency (cycles per second) and itswavelength (metres per cycle),

In vacuum, light travels at a speed of 2.99792458 × 108 m s–1 (3.00 × 108 m s–1 to three
significant figures).
The speed of an electromagnetic wave depends on the nature of the medium through
which the wave is travelling. The speed of an electromagnetic wave in medium (c) is the
product of its wavelength and its frequency.

Another characteristic of a wave is its amplitude, the height of the crest (or depth of the
trough) of the wave. The amplitude of an electromagnetic wave is a measure of the
strength of its electric and magnetic fields. Thus, amplitude is related to the intensity of
the radiation, which we perceive as brightness in the case of visible light.

Figure 6. Amplitude (intensity) of waves.

Light of a particular shade of red, for instance, always has the same frequency and
wavelength, but it can be dim (low amplitude) or bright (high amplitude) Figure 6.
Visible light occupies a small portion of the continuum of radiant energy which is known
as the electromagnetic spectrum (Figure 7). The electromagnetic waves in the different
spectral region travel at the same speed but differ in frequency and wavelength.
The long wavelength, low-frequency portion of the spectrum comprises the microwave
and radio wave regions. The infrared (IR) region overlaps the microwave region on one
end and the visible region on the other.
We perceive different wave lengths (or frequencies) of visible light as different colours,
from red (λ= 750 nm) to violet (λ= 400 nm). Light of a single wavelength is called
monochromatic (Greek “one colour”), whereas light of many wavelengths is
polychromatic (Greek “many colours”). White light is polychromatic.
The region adjacent to visible light on the short-wavelength end consists of ultraviolet
(UV) radiation. Still shorter wavelengths (higher frequencies) make up the X-ray and
gamma ray (γ-ray) regions.
Thus, a TV signal, Infrared (IR) light, and a gamma ray emitted by a radioactive element
differ principally in frequency and wavelength.
Figure 7. Regions of the electromagnetic spectrum.
These wave and particle nature of light is linked by energy since both particle and wave
have energy.
 E=hv , the relationship between energy and frequency
 E= hc/λ, the relationship between energy and wavelength
  E= hvc, the relationship between energy and wave number
The wavelength(λ): is the distance between any two adjacent identical points of
the wave.
The frequency (v) is the number of wave crests passing a given point per unit time; and
is usually expressed in cycles per second or, more commonly, simply as 1/s with “cycles”
understood. It is the number of cycles or oscillations per time.
Wave number: is the reciprocal of wavelength.
Period (T): the time required to complete one complete cycle.
Black body: is a body which absorbs all radiate energy from the sun.
Photon: is a packet of light energy which carries hv amount of quantized energy.
Quantized energy: the motion of the electron is not free. The electron is bound to the
atom by the attractive force of the nucleus and consequently quantum mechanics predicts
that the total energy of the electron is quantized. White light is a combination of light of
many different wavelengths.
When passed through a prism, it is spread into its constituent wavelengths, resulting in a
band spectrum.
A band spectrum resembles a rainbow and contains many different wavelengths of light.
When light from a gas discharge tube is passed through a prism, the result is a line
spectrum.
In contrast to a band spectrum, a line spectrum contains only certain discreet wavelengths
of light.
Example 7. The yellow light given off by a sodium lamp has a wavelength of 589 nm.
What is the frequency of this radiation? 2. A dental hygienist uses X-ray (λ = 1.00 Å) to
take a series of dental radiographs while the patient listens to an FM radio station (λ =
325 cm) and looks out the window at the blue sky (λ = 473 nm). What is the frequency
(in s–1) of the electromagnetic radiation for each source?
Solution:
1. Rearranging Equation 2.1, and ν = co/λ. We insert the value for c and ? and then
convert nm to m. This gives us

2. Because we are provided with the wavelengths, we can find the frequencies from
Equation 2.1. Since co has units of m s–1, we first convert the entire wavelength to
metres.
For X-ray
Exercise 4. Some diamonds appear yellow because they contain nitrogenous compounds
that absorb purple light of frequency 7.23×1014 s–1. Calculate the wavelength (in nm) of
the absorbed light. 2. The FM station broadcasts traditional music at 102 MHz on your
radio. Units for FM frequencies are given in megahertz (MHz). Find the wavelength of
these radio waves in meters (m), nanometers (nm), and angstrom (Å).

1.8. Electronic Configuration and Periodic Table

Electron configuration is the way of filling\distribution of electrons among the given
orbitals. In writing electronic configurations or electron filling of orbitals, we follow the
Aufbau’s principle, Hund’s rule, and the Pauli Exclusion Principle. These are:

A.The Aufbau’s Principle (building up principle): explains the order of filling

electrons in various orbitals of an atom. Filling begins with the orbitals in the lowest
energy, or most stable, shells and Thus, the 1s orbital fills first, then the 2s, followed by
the 2p and the 3s orbitals.
Figure 8. Increasing order of filling orbitals.

B. Hund's rule: It’s Principle: Equal energy orbitals (degenerate orbitals) are each
occupied by a single electron before the second electrons of opposite spin enters the
orbital. In other words, each of the three 2p orbitals (2px, 2py and 2pz) will hold a single
electron before any of them receives a second electron. It states that each degenerate
orbital, (e.g.2px, 2py, and 2pz) must first receive one electron before any of the orbitals
can receive a second electron.

C. Pauli Exclusion Principle: It’s Principle. No two electrons can have the same four
quantum numbers. i.e. they must differ in at least one of the four quantum numbers.
- each orbital contains a maximum of two electrons.

 These two electrons must have opposite values for the spin, which is
generally indicated by showing the electrons as arrows pointing up () or
down ().
Excise 5. write the ground electron configuration of based on example given
The reason for these exceptions to the aufbau principle is not completely understood, but
it seems that the half-filled 3d subshell of chromium (3d5) and the fully filled 3d subshell
of copper (3d10) lends a special stability to the electron configurations. Apparently,
having a half-filled 4s subshell and a half-filled 3d subshell gives a lower energy state for
a Cr atom than having a filled 4s subshell.
Exercise 6
1. Write the electron configuration for the Co3+, Cl– , Al+, Cr, As–, and Cu.
2. Write the electron configuration and the orbital diagram of the first excited state of
sodium. (Hint: The outermost electron is excited).
3. What is the electron capacity of the nth energy level? What is the capacity of the fourth
energy level?

1.9. Periodic table and Periodic Properties of Elements

The periodic law (Modern periodic table) tells us that if we arrange the elements in
order of increasing atomic number, we periodically encounter elements that have similar
chemical and physical properties. Elements in a group have similar chemical and physical
properties, and those within a period have properties that change progressively across the
table.
1.9.1. Classification of the Elements
Representative or main group elements: These consist of all s- and p-block elements.
The chemical properties of the representative elements are determined by the number of
valence electrons in their atoms.
Transition elements: These are d-block elements. There are four series of transitional
elements, 3d, 4d, 5d and 6d depending on the energy levels of d-orbitals.
Inner transition elements: These are the f-block elements. There are two series of f-block
elements, 4f and 5f series called lanthanides and actinides, respectively. The periodic
table is unable to include the inner transition elements in its main frame. They have been
allotted the same single place in the periodic table though their electronic configurations
are not identical. Besides, the variation in their properties is not much.1s
The general properties of metals and nonmetals are distinct. Physical and chemical
properties that distinguish metals from nonmetals are summarized in Table:
S blok elements
IA
IIA p- blok elments
d-blok metals

4f Lanthanide series
5f Acthenide series

Figure 9. the general periodic presentation

s-blockmetals Nobel gas
d-block Lanthanide
p-block metals
Actinide series Metaloid

Nonmetals Hydrogen
Figure 10. the modern periodic table

The vertical columns are referred to as groups or families, and the horizontal rows are
called periods. Elements in a group have similar chemical and physical properties, and
those within a period have properties that change progressively across the table. Several
groups of elements have common names that are used so frequently they should be
learned. The Group IA elements, except H, are referred to as alkali metals, and the
Group IIA elements are called the alkaline earth metals. The Group VIIA elements are
called halogens, which means “salt formers,” and the Group VIIIA elements are called
noble(or rare) gases.

1.9.2. Periodic Variation in Physical Properties

a) Atomic Radii
As we move across the periodic table, atoms become smaller due to increasing effective
nuclear charges. As we move from left to right across a period in the periodic table,
atomic radii of representative elements decrease as a proton is added to the nucleus and
an electron is added to a particular shell.

The effective nuclear charge, Zeff experienced by an electron in an outer shell is less than
the actual nuclear charge, Z. This is because the attraction of outer-shell electrons by the
nucleus is partly counterbalanced by the repulsion of these outer-shell electrons by
electrons in inner shells. This concept of a screening, or shielding, effect helps us
understand many periodic trends in atomic properties. Consider an atom of lithium; it has
two electrons in a filled shell, 1s2, and one electron in the 2s orbital, 2s1. The electron in
the 2s orbital is fairly effectively screened from the nucleus by the two electrons in the
filled 1s orbital, so the 2s electron does not “feel” the full 3 charge of the nucleus. The
effective nuclear charge, Zeff, experienced by the electron in the 2s orbital:

Example;11Na, Zeff =11-10 = +1, 12Mg, Zeff =12-10= +2, 13Al, Zeff =13-10= +3
b) Ionic Radii
Ionic Radii of metals always greater than the corresponding cations because they lost
electrons from shells which reduced electron-electron repulsions. Example;Mg (1.6 Ǻ) >
Mg2+(0.85 Ǻ). Simple negatively charged ions (anions) are always larger than the neutral
atoms from which they are formed because there is addition of extra electron to the shell
which increased electron. Example: Cl- (1.67 Ǻ) > Cl (1.1 Ǻ). Both sizes of cations and
anions decrease from left to right across a period whereas both cation and anion sizes
increase going down a group. Within an isoelectronic series, radii decrease with
increasing atomic number because of increasing nuclear charge.
Isoelectronic ions: ions with the same number of core electrons. Na+, Mg+2, Al+3, F-, O-
2
, N-3 all contain 10 electrons; all have the same electron configuration as Ne but, in
terms of size,
N-3>O-2>F->Na+>Mg+2>Al+3; the ion with the greater number of protons in an
isoelectronic series will be the smallest due to the greater nuclear charge pulling the
electrons in closer.
In general,

Arrange the following ions in order of increasing ionic radii: (a) Ca2+, K+, Al3+ +, (b) Se2-,
Br-, Te2- Answers: a) Al3+< Ca2+ <K , b)Br-< Se2- < Te2-

c) Ionization Energy
Ionization (potential) Energy: the minimum amount of energy required to remove an
electron from ground state (loosely bounded) atom in gaseous state. It measures how
outermost electrons held by the nucleus.
X (g) + IE → X+ (g) + e-

The first ionization energy (IE1), also called first ionization potential, is the minimum
amount of energy required to remove the most loosely bound electron from an isolated
gaseous atom to form an ion with a 1+charge. Elements with low ionization energies (IE)
lose electrons easily to form cations.

General trends in first ionization energies of A group elements with position in the
periodic table. Exceptions occur at Groups IIIA and VIA. The first ionization energies for
the Group IIIA elements (B, Al, Ga, In, Tl) are exceptions to the general horizontal
trends. They are lower than those of the IIA elements in the same periods because the
IIIA elements have only a single electron in their outermost p orbitals. Less energy is
required to remove the first p electron than the second s electron from the outermost
shell, because the p orbital is at a higher energy (less stable) than an s orbital within the
same shell (n value) Effective nuclear charge, Zeff, increases going from left to right
across a period. The increase in effective nuclear charge causes the outermost electrons to
be held more tightly, making them harder to remove. The first ionization energies of the
Group IIA elements (Be, Mg, Ca, Sr, Ba) are significantly higher than those of the Group
IA elements in the same periods. This is because the Group IIA elements have higher Zeff
values and smaller atomic radii. Thus, their outermost electrons are held more tightly
than those of the neighboring IA metals. It is harder to remove an electron from a pair in
the filled outermost s orbitals of the Group IIA elements than to remove the single
electron from the half-filled outermost s orbitals of the Group IA elements. The general
left-to-right increase in IE1for each period is interrupted by a dip between Groups VA
(N, P, As, Sb, Bi) and VIA elements (O, S, Se, Te, Po). Presumably, this behavior is
because the fourth np electron in the Group VIA elements is paired with another electron
in the same orbital, so it experiences greater repulsion than it would in an orbital by itself.
This increased repulsion apparently outweighs the increase in Zeff, so the fourth np
electron in an outer shell (Group VIA elements) is somewhat easier to remove (lower
ionization energy) than is the third np electron in an outer shell (Group VA elements).
The first ionization energies therefore generally increase from left to right across the
periodic table. The order of ionization energies decreased as 3rd > 2nd >1st because it is
too difficult to remove an electron from cation specie.

In general ionization energy increase across the period since Zeff increase by one; the size
of atoms decrease which results the outermost electrons bound tightly with the nucleus.
d) Electron Affinity (EA):

The electron affinity (EA) of an element may be defined as the amount of energy released
when an electron is added to an isolated gaseous atom to form a negative charge.

X (g) + e- → X-(g) + EA

This process can be either endothermic or exothermic, depending on the element. You
can see that many of these elements have negative values of EA, which means that
energy is released when the gaseous atom accepts an electron. However, for some
elements, energy is required for the atom to become negatively charged and the value of
their EA is positive.

Electron Affinity (EA): Energy is always required to bring a negative charge (electron)
closer to another negative charge (anion). So the addition of a second electron to anion to
form an ion with a -2 charge is always endothermic. Thus, electron affinities of anions
are always positive.
X-(g) + e- → X2-(g) + EA
Most elements have no affinity for an additional electron and thus have an electron
affinity (EA) equal to zero. We can represent the electron affinities of helium and
chlorine as

Halogens have ns2-np5 electron cofiguration which are most electron affinities to form
noble gas cofiguration.
 increase except noble gas

decrease

e) Electro-negativity (EN):

The electro-negativity (EN) of an element is a measure of the relative tendency of an

atom to attract electrons towards it when it is chemically combined with another atom.
Elements with high electro-negativities (nonmetals) often gain electrons to form anions.
Example; F (4.0) > O (3.5) > Cl=N (3.0). Elements with low electro-negativities (metals)
often lose electron to form cations.

For the representative elements, electro-negativities usually increase from left to right
across periods except noble gas and decrease from top to bottom within groups

increase except noble gas

decrease
.
Arrange the following elements in order of increasing electro-negativity? B, Na, F, O

answer, Na< B< O< F

f) Metallic character:

Metallic character increases from top to bottom and decreases from left to right with
respect to position in the periodic table. Nonmetallic character decreases from top to
bottom and increases from left to right in the periodic table.

General trends in metallic character of A group elements with position in the periodic
table.
In modern periodic table, elements are arranged as the function of their atomic number.
Main group elements are elements contain s-block metals and p-block metal, metalloid
and nonmetals. This periodic table constructed with the columns (family) and the
horizontal row (periods). Periodicity is the variation of physical properties in periodic
table such as atomic size, electronegativity, ionization energy, metallic character and
others as summarized below.

Advantages of Periodic Classification of the Elements

Some of the advantages of periodic classification of elements are: 1. The classification of
elements is based on the atomic number, which is a fundamental property of an element.
2. The reason for placing isotopes at one place is justified as the classification is on the
basis of atomic number. 3. It explains the periodicity of the properties of the elements and
relates them to their electronic configurations. 4. The position of the elements that were
misfits on the basis of mass number (anomalous pairs like argon and potassium) could be
justified on the basis of atomic number. 5. The lanthanides and actinides are placed
separately at the bottom of the periodic table. 6. The table is simple, systematic and easy
way for remembering the properties of various elements as it is based on the electronic
configuration.
Unit summary
 Cathode rays (electrons) are produced when electricity passes through evacuated
tubes. X-rays form when cathode rays strike matter.
 Radioactivity is the emission of radiation by unstable nuclei, and the most
common types of radiations are alpha (α) particles, beta (β) particles and gamma
(γ) rays. Alpha particles are helium nuclei; beta particles are electrons; and
gamma rays are high frequency electromagnetic radiation similar to X-rays.
 Rutherford's atomic model is that of a very small positively charged nucleus and
extra-nuclear electrons. The nucleus consists of protons and neutrons and contains
practically all the mass of an atom. Atomic masses and relative abundances of the
isotopes of an element can be established by mass spectrometry. The atomic mass
of the element is the average of these mass numbers based on their percentage
abundances Electromagnetic radiation is the transmission of electric and magnetic
 fields as a wave motion. The waves are characterized by their velocity in a
medium: c = νλ. A light source that emits an essentially unbroken series of
wavelength components has a continuous spectrum. Only a discrete set of
wavelength components is present in the emission spectrum of an atom.
 Einstein's explanation of the photoelectric effect views light as packets of energy
called photons. The energy of the photon (Eph) is given by the expression E = hν
where h is Planck's constant.
 Bohr's theory requires the electron in a hydrogen atom to be in one of a discrete
set of energy levels. The fall of an electron from a higher to a lower energy level
releases a discrete amount of energy as a photon of light with a characteristic
frequency.
 Bohr's theory accounts for the observed atomic spectrum of hydrogen atom.
 The electron in a hydrogen atom can be viewed as a matter-wave enveloping the
nucleus. The matter-wave is represented by a wave equation, and solutions of the
wave equation are wave functions. Each wavefunction is characterized by the
value of four quantum numbers: the principal quantum number, n; the angular
momentum quantum number l; the magnetic quantum number, ml; and the spin
quantum number, ms. Wave functions with acceptable values of the three are
called atomic orbitals. An orbital describes a region in an atom that has a high
probability of containing an electron or a high electron change density. Orbitals
with the same value of n are in the same principal energy level or principal shell.
Those with the same value of n and of l are in the same sublevel or subshell. The
shapes associated with orbitals depend on the value of l. Thus, the s orbital (l = 0)
is spherical and the p orbital (l = 1) is dumbbell-shaped.
 The n, l and ml quantum numbers define an orbital, but a fourth quantum number
is also required to characterize an electron in an orbital - the spin quantum
number, ms. This quantum number may have either of two values: +½ or –½.
 The wave mechanical treatment of the hydrogen atom can be extended to multi-
electron atoms, but with this essential difference: principal energy levels are (i)
lower than those of the hydrogen atom and (ii) split, that is, having different
energies for the different subshells.
 Electron configuration refers to the distribution of electrons among orbitals in an
atom. Introduced here are the subshell notations (or "s,p,d, f") and the orbital
diagram. Key ideas required to write a probable electron configuration are: (i)
electrons tend to occupy the lowest energy orbitals available; (ii) no two electrons
in an atom can have all four quantum numbers alike; and (iii) where ever possible,
electrons occupy orbitals singly rather than in pairs.
 The Aufbau principle describes a hypothetical process of building up one atom
from the atom of preceding atomic number. With this principle and the idea cited
above, it is possible to predict probable electron configurations for many of the
elements. In the Aufbau process, electrons are added to the s or p subshell of
highest principal quantum number in the representative or main group elements.
In transition elements, electrons go into the d subshell of the second last shell, and
in the inner transition elements, into the f subshell of the third last shell.
 Elements with similar valence-shell electron configurations fall in the same
group of the periodic table. For A-group elements, the group number corresponds
to the number of electrons in the principal shell of highest quantum number. The
period number is the same as the highest number of principal shell containing
electrons (the outer shell). The division of the periodic table into s, p, d and f
blocks greatly assists in the assignment of probable electron configurations.
 Certain atomic properties vary periodically, when atoms are considered in terms
of increasing atomic number. The properties and trends considered in this unit are
those of atomic radius, ionic radius, ionization energy and electron affinity.
Values of these atomic properties strongly influence physical and chemical
properties of the elements.
Review questions
Part I: Multiple Choice Type Questions
1. The number of neutrons in an atom of 226 88Ra is:
a. 88 b. 82 c. 138 d. 314
2. Which of the following are usually found in the nucleus of an atom?
a. Protons and neutrons only b. Protons, neutrons and electrons
c. Neutrons only d. Electrons and neutrons only
3. An atom has an atomic number of 31 and a mass numbers of 70. How many
electrons will it have in its valence shell?
a. 5 b. 4 c. 3 d. 2
4. Which of the following would produce a line spectrum rather than a continuous
spectrum?
a. Sunlight b. Excited hydrogen atom
c. A normal filament light bulb d. A yellow (sodium) street light
5. Among the following, which colour corresponds to light of the highest frequency?
a. Green b. Red c. Yellow d. Blue
6. Which one of the following is not a valid electronic configuration?
a. 2, 8, 8, 2 b. 2, 8, 9, 1 c. 2, 6 d. 2, 8, 4
7. Which of the given elements will have the electronic configuration?
1s22s22p63s23p64s2.
a. Neon atoms b. Chlorine atoms c. Magnesium ion d. Calcium atoms
8. Which of the following elements has the lowest first ionization energy?
a. Potassium b. Sodium c. Calcium d. Argon
9. How many 3d electrons are present in the ground state of chromium atom?
a. 9 b. 4 c. 6 d. 5
10. The first ionization energy of aluminium is slightly lower than that of magnesium
because:
a. magnesium has a higher nuclear charge
b. the outer electron in aluminium is in a p-orbital not an s-orbital
c. in aluminium the electron is being lost from a doubly filled orbital
d. the radius of the aluminium atom is greater than that of the magnesium
atom
11. Which of the following atoms would have the highest fourth ionization energy?
a. P b. Si c. N d. C
12. How many unpaired electrons are there in the Cr3+ ion?
a. 6 b. 3 c. 1 d. 0
13. Which of the following species would require the highest energy for the removal of
one electron?
a. Mg2+ b. Na+ c. Ne d. F–
14. Which of the following has the lowest electronegativity?
a. Carbon b. Magnesium c. Beryllium d. Boron
15. Which of the following has the smallest radius?
a. Na b. Na+ c. Mg d. Mg2+
Part II: Answer the following questions:
16. Identify the following subatomic particles:
17. The number of these in the nucleus is equal to the atomic number.
18. The particle that is gained or lost when ions are formed.
19. The particle that is not found in the nucleus.
20. The particle that has no electrical charge.
21. The particle that has a much lower mass than the others.
22. Calculate the number of protons, neutrons and electrons in the following:

23. Carbon has atomic number 6. It comprises three isotopes, the first with 6 neutrons,
the second with 7 neutrons, the third with 8 neutrons.
24. Calculate the mass numbers of the three isotopes and represent them in the form of
xCy
25. Explain what is meant by “isotope”
63 65
26. In naturally occurring copper isotopes, 29Cu contributes 69.09% and 29Cu,

30.91%. Calculate the relative atomic mass of copper. (Accurate mass determined;
63
29Cu = 62.9298 mu, 6529Cu = 64.9278 mu)
27. Two particles X and Y have the following composition: X: 17 protons, 18 neutrons,
17 electrons Y: 17protons, 18 neutrons, 18 electrons
28. What is the relationship between these particles?
29. Will these two particles have similar chemical properties? Explain why?
30. Arrange the following in order of increasing ionization energy: Li, Na, Ne, N, O
31. Explain the following:
32. The first ionization energy of beryllium is greater than that of boron.
33. The first ionization energy of oxygen is less than that of nitrogen.
34. The first ionization energy of lithium is greater than that of sodium.
35. The electron configuration of a particular metal cation M3+ is [Ar] 3d 2.
36. Identify the corresponding metal.
37. Write the electron configuration of the metal atom.
38. Arrange the following in order of increasing atomic radius Mg, Cs, Ca, Al, Ba.
39. Explain briefly, why potassium always occurs as a +1 ion in its compounds and
calcium as a +2 ion.
40. Arrange the atoms (ions) in each of the following groups in order of increasing size
based on their location in the periodic table.
a. Mg2+, O2–, Na+, F –, Al3+ b. Ne, N3–, F –, Na+, C 4–
c. F, Be, C, B, Li d. K+, S2–, As3–, Cl–, Ca2+
41. Excited sodium atoms emit light with a wavelength of 589 nm. Calculate the:
a. frequency of the light, and b. energy of one of these photons
in joules
42. A hydrogen atom is excited to the n = 8 energy level. It emits a photon of light as it
falls to the n = 2 energy level. Calculate the:
a. wavelength of light emitted, and b. frequency of the light
emitted
43. The electron of a hydrogen atom is in the n = 3 level. What is its energy?
44. Calculate the wavelength of the light emitted when an electron falls from n = 3 to
the n = 1 state in hydrogen atom.
45. The photon emitted by a cyclotron has a velocity of 1.50 × 103 m s–1. What is the
wavelength of this photon? Given that the mass of photon = 1.676 × 10–27 kg and
Planck’s constant = 6.62 × 10–34 J.s.
46. Write the number and the letter for the orbital that corresponds to the following
pairs of n and l quantum numbers:
a. n = 3, l = 1 b. n = 4, l = 0 c. n = 3, l = 2 d. n = 5,
l=3
47. Write the electron configurations for the following atoms and ions:
a. Fe3+ b. V c. Cr3+ d. Al3+
48. Identify the transition element (s) from the following:
a. 40Zr b. 88Ra c. 56Fe d. 36Kr