2021-02-18

ATOMIC STRUCTURE
 Properties of light
 Photoelectric effect
 Electromagnetic radiation

 Bohr model of Hydrogen atom

 Electron transitions & transition series
 Successes and Failures of Burh model

 Wave function model of many-electron Atom

 Quantum numbers
 Atomic orbitals and orbital shapes
 Electron configuration
 Radial probability function
 Orbital penetration and shielding effect

ATOMIC STRUCTURE
 Electrons

 Electrons are found in the region

around the nucleus

 Chemical and physical properties

are due to electron structure of atom

 Energized atoms emit light

 To fully understand the atom we

must first explore light and the
transfer of energy

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 2021-02-18

ATOMIC STRUCTURE
 Light as a wave

 Wavelength (λ) is the distance between two repeating waves

 Amplitude (A) is the value of wave disturbance
 Frequency (ν) is number of oscillations per second
 The three properties of the wave are related by the equation

λν = C
where, C = speed of light = 2.9979 x 108 m/s

 Example:
Calculate the wavelength of a wave oscillating at 1.2 x 107 Hz

ATOMIC STRUCTURE
 Max Planck and Black body radiation
 Ancient scientists believed that change in radiant energy between two states
was continuous.
 Max Plank used black body radiation experiment to postulate
1. That radiant energy is not emitted in a continuous fashion
2. That radiant energy is emitted in bundles called Quanta (singular Quantum)
3. That the energy E of a quantum of radiation is proportional to the frequency of
radiation as shown:
E α ν
E = hν
where: E = energy, ν = frequency and h = Plank’s constant (6.6262 x 10-34 J.s)

4. Combining the equation of the wave and Planck’s equation we get

hc
E

Note: Energy is inversely proportional to wavelength

5. Example:
A HeNe laser lamp operate at 628nm, what is the quantum of energy emitted?

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 2021-02-18

ATOMIC STRUCTURE
 Light as a particle (photoelectric effect)
 Albert Einstein proposed that light composed of particles called photons
1. He proposed photoelectric effect to explain his theory

Light Photons

Metal

2. When light of certain wavelength shines on a metal, photons are emitted.

3. The kinetic energy (KE) of the photon is proportional to the frequency of the light
used to irradiate the metal as shown
Ephoton = Emin + KEe-

Where;
KE = Kinetice Energy
Emin = Eionization = work function = Energy required to bring from the bulk of the metal to the
surface.

Example: A metal has a work function of 280 kJ/mol. What is the maximum kinetic
energy of the ejected electron if the wavelength of the incident light is 209 nm?

ATOMIC STRUCTURE
 Wave – Particle Duality
 In a related study to photo electric effect, Einstein explained relativity in
which he showed that
E = mc2
where E = energy, m = mass and c = speed of light

 Combining the wave equation (E =hc/λ) and relativity equation (E = mc2)

mphoton = h/λc
 We conclude that photons have mass and they are also waves. This is
known as “wave-particle duality”

 Example:
Calculate the mass of a photon with a wavelength of 300nm

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ATOMIC STRUCTURE
 Particles as wave
 Louis de Broglie proposed that
1. If photons which have wave properties also have mass (particle like properties) then
any particle should also have wave-like properties

2. From the equation (m = h/λc ), he derived the equation for wavelength of any moving
particle by replacing the speed of light c with velocity ν of the particle

h
de Broglie wavelength   
m
where Λ = de Broglie wavelength, m = mass of particle, ν = velocity of particle and h =
Planck’s constant

3. The conclusion is that ALL matter has both particle-like and wave-like properties

4. Example: Calculate the wavelength of a particle 9.1 x 10-31 kg moving at a

speed of 2.2 x 106 m/s, mass of electron = 9.1 x 10-31 kg

ELECTROMAGNETIC RADIATION
Radiation Wavelength
(nm)
Short waves 300 to 30000
Microwaves, Radio,
Radar, TV,FM AM

Infrared 780 to 3000

Visible 380 to 780

Ultraviolet (UV) 10 to 380

X-Ray 10-4 to 10
hc
E
 Gamma Rays 0 to 10-4
Note: The energy is inversely proportional to wavelength
1. The longer the wavelength, the lower is the energy and vice versa
2. For example, in the visible region of the spectrum
• Red color has the lowest energy, longest wavelength
• Purple color has the highest energy, shortest wavelength

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 2021-02-18

BOHR MODEL OF Hydrogen ATOM

 Neils Bohr developed a quantum model for a hydrogen-like atoms
1. Electrons circle the nucleus in an orbit – just like earth orbits the sun
2. But a charge moving in a circular path should lose energy by emitting radiation
3. If orbiting electrons lose energy, then they should end up spiraling into the nucleus –
which does NOT happen

 Bohr borrowed the idea of quantized energy from Planck and proposed the
n=1 following assumptions:

n=2 1. That only a certain radii, corresponding to certain energies are allowed
2. He explained that electrons orbiting these allowed orbits
n=3
i. Have definite energy states
ii. Will not radiate energy
iii. Will not spiral into the nucleus

3. He concluded that if orbits of the electrons are restricted, then the energy of the
electrons is also restricted and is given by

 1 
E n   RH Z 2  2 
n 
where RH = Rydburg constant = 2.18 x 10-18 J, n = allowed orbit or energy level and Z =
the number of protons in the nucleus

ELECTRON TRANSITION
 1 
nf nf E f   RH Z 2  2 
n 
 f 
ΔE = +hν
ni
 1 
ni Ei   RH Z 2  2 

 ni 

Supply energy = +hν   E f  Ei   hv

 1 1 
 E   RH Z 2  2  2 
n ni 
 f

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ELECTRON TRANSITION
 Important points to note:
 The equation

 1 1 
 E   RH Z 2  2  2 
n n 
 f i 

1. Was developed for one-electron atom, where there is only one electron in an atom or ion but
many number of protons are possible

2. Some examples of one-electron atoms/ions are : H, He+, Li2+ , Be3+ … etc

3. If nf > ni, the electron absorbs energy (excited) and E > ZERO = Positive (Absorption)

4. If nf < ni, the electron loses energy (relaxes) and E < ZERO = Negative (Emission)

5. Ionization implies nf = ∞

6. We can use the equation above to calculate the energy absorbed or emitted during a transition

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ELECTRON TRANSITION
 Examples:

1. Calculate the wavelength of energy needed to excite hydrogen electron from

n = 1 to n = 2

2. Calculate the ionization energy of He+ in kJ/mole

3. Ground state He + absorbs a photon to promote electron to excited state. This

electron then relaxes to n=2 my emitting a photon with 121.61 nm wavelength.
What is the original n-level of the electron?

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ELECTRON TRANSITION SERIES

ni

ΔE = -hν

nf

Energized (excited) electron

• Consider only emission process
1. Electrons relax from higher
energy to lower energy level
2. If nf = 1 Lyman series
3. If nf = 2 Balmer series
4. If nf = 3 Paschen series
5. If nf = 4 Brackett series
6. If nf = 5 Pfund series

Example:
A Paschen series emission occurs at 1.283 µm. What is the initial quantum level of the electron

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LIMITATIONS OF BOHR MODEL

 Despite its success, Bohr model has some serious limitations:
1. It only works for one-electron atom or ions
2. Could not be extended to explain the periodicity of elements
3. Electrons do not move in a circular orbit.
4. Electron does not always remain at a fixed distance from the nucleus

 Despite its limitations, Bohr model introduces TWO important ideas.

1. Energy of electron is Quantized, i.e., electrons exist only in certain energy
level described by n
2. Energy gain or loss is responsible for moving electrons from one energy
level to the other.

 Bohr model was replaced by wavefunction model (the present view of

the atomic structure)

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