UNIT 1

Atomic structure and interatomic bonding 12h

Electrons in atoms, Bohr atomic model, wave mechanical model, introduction to

quantum chemistry, wave functions and probability densities, quantum numbers,
orbital shapes - s,p,d,f- LCAO-MO of H2, covalent, ionic and metallic bonding,
bonding forces and energies, lattice energy and Madelung constant, metallic crystal
structure, ceramic crystal structure and influencing factors.
Ernest Rutherford and the
gold foil experiment
 Rutherford atom
 Drawback of Rutherford atom:

• The nuclear model explained Rutherford's experimental results, but it

also raised further questions.

• For example, what were the electrons doing in the atom?

• How did the electrons keep themselves from collapsing into the
nucleus, since opposite charges attract?

According to Maxwell’s
theory, a Rutherford
atom would only survive
for only about 10-12 secs
 Timeline

atoms
were
uniform,
solid,
hard,
incompres
sible, and
indestructi
ble
 The planetary model of the
atom
 At the beginning of the 20th century, a new field of study known as
quantum mechanics emerged.

 One of the founders of this field was Danish physicist Niels Bohr, who
was interested in explaining the discrete line spectrum observed when
light was emitted by different elements.

 Bohr was also interested in the structure of the atom, which was a
topic of much debate at the time.

 Numerous models of the atom had been postulated based on

experimental results including the discovery of the electron by J. J.
Thomson and the discovery of the nucleus by Ernest Rutherford.

 Bohr supported the planetary model, in which electrons revolved

around a positively charged nucleus like the rings around Saturn—or
alternatively, the planets around the sun.
 The planetary model of the
atom

Many scientists, including Rutherford and Bohr, thought electrons

might orbit the nucleus like the rings around Saturn
 The planetary model of the
atom
However, scientists still had many unanswered questions:

 Where are the electrons, and what are they doing?

 If the electrons are orbiting the nucleus, why don’t they fall
into the nucleus as predicted by classical physics?

 How is the internal structure of the atom related to the

discrete emission lines produced by excited elements?

 Bohr addressed these questions using a seemingly simple

assumption: what if some aspects of atomic structure, such as
electron orbits and energies, could only take on certain values?
 Quantization and photons
 By the early 1900s, scientists were aware that some phenomena occurred
in a discrete, as opposed to continuous, manner.

 Physicists Max Planck and Albert Einstein had recently theorized that
electromagnetic radiation not only behaves like a wave, but also
sometimes like particles called photons.

 Planck studied the electromagnetic radiation emitted by heated objects,

and he proposed that the emitted electromagnetic radiation was
"quantized" since the energy of light could only have values given by the
following equation:
E= nhν
where n is a positive integer
h is Planck’s constant = 6.626 X 10-34 J/s
ν is the frequency of the light, which has units of s-1
 Quantization and photons

 As a consequence, the emitted

electromagnetic radiation must have
energies that are multiples of hν.

 Einstein used Planck's results to explain

why a minimum frequency of light was
required to eject electrons from a metal
surface in the photoelectric effect.

 When something is quantized, it means

that only specific values are allowed.
 Quantization and photons

 Light consists of electromagnetic waves. Electromagnetic radiation

includes the following spectrum.
 Bohr's Idea

Bohr combined the elements of

classical physics with the ideas of
quantum mechanics. Thus his
model is a hybrid that spanned
the gap between the physics of
Newton and the newly emerging
quantum physics.
 Bohr's model of the hydrogen
Bohr's model of the hydrogen atom is atom
based on four assumptions.
 Bohr's Idea
The next two assumptions are more general:
Electrons do not give off electromagnetic radiation
when they are in an allowed orbit. Thus, the orbits are
stable.
Electromagnetic radiation is given off or absorbed
only when an electron changes from one allowed orbit
to another. If the energy difference between the two
allowed orbits is ΔE, then the frequency, f, of the
photon that is emitted or absorbed is given by ΔE = hf.

“Allowed”
orbits
 Bohr's model of the hydrogen
atom
o Bohr's model retains the classical picture of an electron
orbiting a nucleus. It also adds the quantum requirements
that only certain orbits are allowed and no radiation is
given off from these orbits.
o To determine the allowed Bohr orbits—those with specific
radii and specific energies—we apply two conditions.
o First, the electron moves in a circular orbit of radius r and
speed v

As a result, the electron experiences a

centripetal acceleration toward the nucleus
of magnitude a = v2/r.
From Newton's second law of motion, we
know that a force, F = ma, is required to
produce an acceleration. In this case, the
force is the electrostatic force F = ke2/r2.
 Bohr's model of the hydrogen
atom

As a result, the electron experiences a

centripetal acceleration toward the nucleus
of magnitude a = v2/r.
From Newton's second law of motion, we
know that a force, F = ma, is required to
produce an acceleration. In this case, the
force is the electrostatic force F = ke2/r2.
Bohr's model of the hydrogen
atom
Combining these results yields the
following relationship:

F = ma
ke2/r2 = mv2/r
Next, Bohr assumed that the angular
momentum in an allowed orbit must be
an integer n (the quantum number)
times h/2π,
where h is Planck's constant.

Since the electron moves with a speed v

in a circular path of radius r, its angular
momentum is L = mvr.
Thus this condition is
Ln = rnmvn = nh/2π
 Bohr's model of the hydrogen
atom
Combining the force and angular momentum equations allows us
to solve for the radii of allowed orbits. The result is
rn = (h2/4π2mke2)n2 n = 1, 2, 3, …
Substituting the known values for h, π, m, k, and e yields the
following result:
 Bohr's model of the hydrogen
The radius of the first Bohr orbit, which corresponds to
atom
n = 1, is
r1 = 5.29 x 10−11 m
This is known as the Bohr radius. It sets the typical size of a
hydrogen atom. The higher orbits in the Bohr model increase in
radius as n2, as indicated in the figure
 Bohr's model of the hydrogen
atom
 By keeping the electrons in circular, quantized orbits around the
positively-charged nucleus, Bohr was able to calculate the energy of an
electron in the nth energy level of hydrogen:

where the lowest possible energy or ground state energy of a hydrogen

electron E(1) is -13.6 eV.

 The energy is always going to be a negative number, and the ground

state, n = 1, has the most negative value. This is because the energy of an
electron in orbit is relative to the energy of an electron that has been
completely separated from its nucleus, n = ∞ which is defined to have an
energy of 0 eV.

 Since an electron in orbit around the nucleus is more stable than an

electron that is infinitely far away from its nucleus, the energy of an
electron in orbit is always negative.
 Absorption and emission

 Bohr could now precisely describe the

processes of absorption and emission in
terms of electronic structure.

 According to Bohr's model,

an electron would absorb
energy in the form of
photons to get excited to a
higher energy level as long
as the photon's energy was
equal to the energy
difference between the
initial and final energy
levels.
 Absorption and emission
 After jumping to the higher energy level—also called the excited state—the
excited electron would be in a less stable position, so it would quickly emit a
photon to relax back to a lower, more stable energy level.

 The energy of the emitted photon is equal to the difference in energy between the
two energy levels for a particular transition. The energy difference between
energy levels nhigh and nlow can be calculated using the equation for E(n) from the
previous section:
 Absorption and emission

 Since we also know the relationship between the energy of a photon and its
frequency from Planck's equation, we can solve for the frequency of the emitted
photon:
Bohr's model of the hydrogen
atom
 Drawback of Bohr’s Model

 The Bohr model worked beautifully for explaining the hydrogen atom and
other single electron systems such as He+2. Unfortunately, it did not do as
well when applied to the spectra of more complex atoms. It could not
elaborate spectra of multi-electron atoms.

 The Bohr model had no way of explaining why some lines are more intense
than others or why some spectral lines split into multiple lines in the
presence of a magnetic field—the Zeeman effect and Stark effect.

 Wave nature of electron was not justified by the model.

 It violated Heisenberg’s Principle which said that it was impossible to

evaluate the precise position and momentum of electron simultaneously,
only their probability could be estimated.
Atom
 Atom

Atom

Negatively
Nucleus Electrons Charged

Protons Neutrons

Positively Electrically
Charged Neutral
 Atom

 Protons and neutrons have the same mass, 1.67 X10-27 kg

 Mass of electron is 9.11 X10-31 kg

 Atomic Number (Z) and
Atomic Mass (A)

Number Atomic
of Number
Protons (Z)

Mass of Mass of Atomic

Protons Neutrons Mass (A)
Atomic Number (Z) and
Atomic Mass (A)
Isotopes
Isotopes
 Isotopes

Average mass
% abundance % abundance mass
Atomic of
mass of = ( of
Isotope #1
x Isotope
) + ( of
Isotope #2
x of
Isotope #2
) + …
an element #1

Example:
 Questions:

Q1. How many neutrons does this atom of carbon have?

Q2. What evidence did Dalton use to argue for the existence of atoms?

Q3. Explain how Thomson discovered negatively charged particles smaller

than atoms.

Q4. What is the energy required to excite an electron from the third to fifth
Bohr orbit in hydrogen?

Q5. What will be the energy of the emitted photon when an electron in Be+3
ion returns from n = 2 level to ground state.