Atomic Structure I & II

Bohr’s Atomic Theory

In 1913, Niel Bohr came up with a new model for the structure of an atom. He
made the following proposals:

1. Electrons are arranged and moves around the nucleus in concentric circular
paths called orbits. The motion of the electrons is like that of the
planets around the sun. (NB: Because of this proposal, the Bohr’s model
of the atom is referred to as the Planetary Model)
2. The electrons move around the nucleus with a fixed set of allowable energy
which prevents the electrons from falling or crashing into the nucleus.
This fixed set of energies possessed by the electrons is called energy
levels. An electron will remain in it’s orbit and will not fall or collapse
into the nucleus as long as the electron does not lose this fixed set of
energy.
3. An electron can move from one energy level to the next higher one provided
it gains a fixed amount of energy called quantum of energy.

Bohr’s Model of the Atom

Bohr described the atom as a small, dense

nucleus surrounded by orbiting electrons. The
movement of the electrons around the nucleus
is similar to the structure of the Solar
System where the planets are revolving around
the sun.

Energy Level of an electron

It is the region or volume of space around the nucleus of an atom where an

electron is likely to be moving.

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The energy levels in an atom can be compared to a

ladder with a number of rungs. Each rung can be
compared to one energy level. Just as a person
can move from one rung to the other – from up to
down or down to up – so can the electrons move or
jump from one energy level to the other.

Again, just as a person cannot stand in between

the rungs of a ladder, the same way, electrons in
an atom cannot stop between the energy levels. In
order for an electron to move from one energy
level to another, the electron must gain or lose
the right amount of energy. This fixed amount of
energy is called quantum.

A Quantum of Energy
It is the minimum amount of energy required by an electron to move from one
energy level to the next higher energy level. The higher the energy level
occupied by an electron, the more energy it possesses and the farther away from
nucleus. From the diagram above, the first energy level is n=1 and it is the
energy level closest to the nucleus. Electrons found in that energy level has
the least energy since it is closest to the nucleus. An electron found in energy
level, n=3 has higher energy than an electron in energy level, n=2 and so on.
Also, the energy level n = 4, for example, is bigger or larger than n = 3 and
so on. Unlike the rungs of a ladder, the energy levels in an atom are not equally
spaced as can be seen from the diagram above.

The Atomic Emission Spectra

Elements or atoms emit light when they are heated or an electric charge is passed
through them. When heat or electric charge is applied to an atom, the electrons
in the atom absorb the energy (quantum of energy) causing the electrons to move
from their present energy level (stationary state or ground state) to a higher
energy level (excited state). As the electrons drop or fall back from the higher
energy level into their ground state energy level, they lose the quantum of
energy earlier absorbed. This energy is released or lost in the form of light.
Thus, there is the emission of light of different frequencies. The color of
light seen corresponds to the frequency of the emitted light.
When this emitted light is passed through a glass prism, a spectrum of light
with different frequencies are produced called the atomic emission spectrum.
Atomic emission spectrum (pl. spectra) is a pattern of frequencies obtained by
passing the light emitted by atoms of an element in the gaseous state through a
glass prism.

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There are two types of emission spectrum:

1. Continuous spectrum: It is a spectrum in which the range of radiation of

different frequencies pass smoothly from one to the next without any lines
or breaks. Continuous spectrum is produced when white light is passed
through a prism. This spectrum is like the rainbow produced when sunlight
is dispersed by raindrops. It contains all the wavelength of visible light.

2. Discontinuous or Line Spectrum: It is a spectrum in which the range of

radiation of different frequencies are separated with few lines or breaks
from one frequency to the next. The emission spectrum from atoms (that is,
atomic emission spectrum) are said to be discontinuous. This is because,
their spectrum consist of lines or breaks between the different frequencies.
The emission spectrum of each element is unique to that element. Hence, the
emission spectrum of an element can be used to identify the element.
Let’s consider the atomic emission of the hydrogen atom. That is, when the light
produced from a hydrogen atom is passed through a glass prism.

From the diagram above; there are few lines produced, each of which corresponds
to a discrete or specific wavelength.

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Significance of the line spectrum of the hydrogen atom

It indicates that only certain energies are allowed for the electron in the
hydrogen atom. Thus, the energy levels are said to be quantized. This means, if
any energy level were allowed, the emission spectrum would be continuous.

The Wave Motion of Matter

Louis de Broglie, in 1924 predicted that all matter exhibits wavelike motions.
A wave has three primary characteristics: wavelength, frequency and speed. De
Broglie derived an equation called the de Broglie’s equation, that described
the wavelength, λ, of a moving particle or photon:

h
λ =
mv
where h is Planck’s constant (6.6262 × 10 -34 J s), m is mass of the particle and
v is the velocity of the particle. This equation is very useful in calculating
the wavelength of a moving electron in its orbit.
He also described the energy of a particle or photon in an electromagnetic
radiation as:

hc
Ephoton = hv =
𝜆
The frequency, v, of an electromagnetic radiation in relation to the particle
or photon wavelength, λ, and speed, c, is given as:
c
λ =
v

Sample Question:

1. Calculate the wavelength for an electron with mass 9.11 x 10-31 kg

traveling at a speed of 1.0 x 10 7 m/s. Take Planck’s constant, h,
= 6.626 x 10-34 J.s

Solution: h = 6.626 x 10-34 J.s or 6.626 x 10-34 kg.m2/s

h
λ =
mv
λ = 7.27 x 10-11 m

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 Atomic Structure I & II

The Quantum Numbers of an Atomic Orbital

The Bohr’s model of the atom describes electrons to be in fixed energy levels,
that is, electrons are quantized. However, the exact position and momentum of
an electron around the nucleus of an atom is uncertain. To explain this, a new
concept was developed called the Wave Mechanical model or the Quantum Mechanical
model.

According to this model; the position of an electron in an atom is described as

a probability. That is, electrons are considered to form a cloud of negative
charges. Hence it is difficult of say exactly where an electron is located. This
concept is known as the Heisenberg Uncertainty Principle: It states that; it is
not possible to determine exactly both the position and momentum of an electron
moving in an atom. It was proposed by Werner Heisenberg.
Each of the electron cloud where an electron is likely to be located has a shape
which can be calculated using mathematical expressions. This cloud shape is
called an atomic orbital.

An Atomic Orbital
It is a region in space around a nucleus of an atom where there is a high
probability of locating or finding an electron. There are 4 mathematical
expressions or numbers that are used to define the allowed orbitals and describe
the behaviour of the electron in the orbital. These numbers are called Quantum
numbers. The four quantum numbers are:
1. Principal Quantum Number (n)
2. Angular Momentum or Azimuthal Quantum Number (l)
3. Magnetic Quantum Number (ml)
4. Spin Quantum Number (ms)

Principal Quantum Number (n)

This quantum number specifies the energy an electron possess and the size of
the energy level. The principal quantum numbers are assigned values of:
n = 1,2,3,4 … 8. The higher the n value, the higher the energy of the electron
and the farther away the electron is from the nucleus.

Angular Momentum or Azimuthal Quantum Number (l)

The energy levels in an atom are divided into energy sublevels or atomic
orbitals. The angular momentum quantum number specifies the shape of an orbital
in a particular energy level. They are assigned values of (n-1). Thus; l = 0, 1,
2, 3 ….7. A principal quantum number of 1 (i.e. n = 1 ), corresponds to an
angular momentum, l, value of 0 (n-1).

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When l = 0, the shape of the orbital or

sublevel is described as spherical. Hence the
orbital is called the s-orbital. l = 1 gives
an orbital shape called dumb-bell (p-
orbital). When l = 2, the orbital is called
the d-orbital. Orbitals with l = 3 is called
f-orbital. The energy of the subshell
increases with l (s < p < d < f). The d-
orbitals and f-orbitals have complex shapes.

Magnetic Quantum Number (ml)

This quantum number specifies the orientation in space of a particular orbital
of a given energy level, n, and shape, l. The formula for ml = (2l + 1). It can
be used to calculate the number of orientations of a particular orbital. For
example, when l = 0, then the number of orientations of this orbital is 1
(i.e. ml = 2(0) + 1 = 1). Hence, the allowable values of the magnetic quantum
number, ml, is 0.
When ml = 0 for a particular orbital,
it means that the orbital has only
one orientation in space. Hence, the
s-orbital (ml = 0) has only one
orientation in space.
When ml = 3, it means the orbital has
three orientations in space (i.e.
-1, 0, +1). Hence, the p-orbital
(ml = 3) has three different
orientations in space. The energy
and shape of the orbital is however
the same. It is only the
orientations of the orbital that are
different.
Spin Quantum Number (ms)
This quantum number specifies the direction of the spin axis of an electron. An
electron in an orbital can spin in only one of the two directions: m s = +1/2 or
-1/2 (sometimes called up and down).

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Summary of Quantum Numbers

n l ml ms
(= n-1) (= 2l+1)
1 0 0 +½ or -½

(s) (one orbital)

2 1 -1, 0, +1 +½ and -½

(p) (three orbitals)

3 2 -2,-1,0,+1,+2 +½ and -½

(d) (five orbitals)

4 3 -3,-2,-1,0,+1,+2,+3 +½ and -½

(f) (seven orbitals)

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