CHAPTER 2 - ATOMIC STRUCTURE

CHAPTER 2
ATOMIC STRUCTURE

CHEMISTRY UNIT
KOLEJ MATRIKULASI MELAKA

SHARED BY MISS DALINA BINTI DAUD

CHAPTER 2

ATOMIC STRUCTURE

2.1 Bohr’s Atomic Model
2.2 Quantum Mechanical Model
2.3 Electronic Configuration

2

2.1 Bohr’s Atomic
Model

3

2.1 Bohr’s Atomic Model

At the end of this topic students should be
able to:

1) describe the Bohr’s atomic model

2) explain the existence of electron energy levels
in an atom and calculate the energy of electron

3) describe the formation of line spectrum of
hydrogen atom

4) calculate the energy change of an electron
during transition

5) calculate the photon of energy emitted by an
electron that produces a particular wavelength
during transition

4

6) perform calculation involving the Rydberg
equation for Lyman, Balmer, Paschen,
Brackett and Pfund series

7) calculate the ionisation energy of hydrogen
from Lyman series

8) state the limitation of Bohr’s Atomic Model.
9) state the dual nature of electron using de

Broglie’s postulate and Heisenberg’s
uncertainty principle

5

BOHR’S ATOMIC MODELS

In 1913, a young Dutch physicist,
Niels Böhr proposed a theory of atom
which he described that electrons
circling a central nucleus which
contains positively charged protons.
Böhr also proposed that these orbits
can only occur at specifically
“permitted” levels only according to
the energy levels of the electron and
explain successfully the lines in the
hydrogen spectrum.

6

BOHR’S ATOMIC MODELS

Bohr postulates (assumptions) are :

1. Electron moves in circular orbit about the
nucleus . It does not radiate or absorb energy
while moving around the nucleus.

H Nucleus 11H
(proton)

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2. The moving electron in the permitted orbit has
a specific amount of energy (quantized
energy).

• Orbit is a pathway of an electron travels around the
nucleus of an atom

• [ orbit = energy level = shell ]

e

orbit
Nucleus
(proton)

n=1

n=2
n=3

8

• The energy of an electron at its orbit ( energy level)

is  RH
n2
En 

Where:

n = the number of particular orbit / energy level/ quantum
number ,1, 2, 3, …∞

RH = Rydberg’s constant, 2.18 x 10-18 J

Note:
• n identifies the orbit of electron
• Energy is zero if an electron is located infinitely far from

nucleus

9

Energy of an electron is quantized , it has a specific
value

If an electron occupies Electron orbiting the
n=4, it has the energy of: nucleus at n=1 has the
energy of E1 = -RH
E4= -RH
42 12

e

nucleus

n=1

n=2
n=3
n=4

10

Example

1. Is it likely that there is an energy level, n for a
hydrogen atom when En = -1.00 x 1028 J?

2. Calculate the energy of an electron at energy

level

i) n = 2 ii) n = 5

Answer : ii) -8.72 x 10-20 J
1. no, n = 1.47 x 10-23
2. i) -5.45 x 10-19 J

11

Solution

1. En   RH
n2

 1.00 x 10 28   2.18 x 10 18 J
n2

n2   2.18 x 10 18 J
 1.00 x 10 28 J

n  1.48 x 10 23

12

Solution E2   RH
n2
2. i)
  2.18 x 10 18 J
2. ii) 22

  5.45 x 10 19 J

E5   RH
n2

  2.18 x 10 18 J
52

  8.72 x 10 20 J

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3. At ordinary conditions the electron is at the
ground state (lowest level).
If energy is supplied, the electron absorbed
the energy and is promoted from a lower to a
higher energy level. (Electron is excited)

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3. A specific amount of energy is
absorbed by an electron
E = h = E3-E1 (+ve)

• Electron is excited from lower to
higher energy level.

e

n =1 n = 2 n = 4
n=3

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4. Electron at its excited states is unstable. It will
fall back to a lower energy level and releases a
specific amount of energy in the form of light
(radiation), called a photon.

The energy of the photon equals to the energy
difference between the levels, ΔE.

photon = ΔE

16

4. Electron falls from higher to lower energy level releases
a photon.
E = h = E1-E3 (-ve)

e n =1 n = 2 n = 4
n=3
photon, h

17

Fig. 7.10

10 August 2021 Atomic structure 18

Energy level diagram for the hydrogen atom

Potential energy n=

n=4
n=3

n=2

Energy Energy
absorbed released

n=1

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• The amount of energy emitted (released) when the
electron falls can be determine by

Energy released = the energy difference between
E two energy levels, Ef - Ei

where E = Ef - Ei

Ef  RH 1  and Ei  RH  1 
nf2  ni2 

E  RH 1     RH 1  
nf2   ni2  

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Thus, R H  

E  1  1
ni2 nf 2

Where:
ni = energy level at initial state
nf= energy level at final state
RH=Rydberg constant, 2.18 x 10-18 J

21

• The photon i.e the amount of energy released ,
E by the electron transitions between two energy
levels has an appropriate frequency,  and

wavelength, 

E = h h (Planck’s constant) = 6.63 10-34 J s
 = frequency

and   c c (speed of light) = 3.00108 ms-1


Thus,

ΔE  hc



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Example

One mole of electron drops from the forth
energy level to the third energy level.
Calculate:

a) the energy of the photon emitted
b) the frequency of this photon

23

Solution

electron drops from the forth energy level to the third
energy level.

i) ni = 4 nf = 3

E  RH ( 1  1 )
ni 2 nf 2

=2.18x10-18 J  1 1 
 42 - 32 

=-1.06x10-19 J

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ii) frequency, Ʋ

  E

h
1.06x10-19 J
= 6.63x10-34Js

1.60x10 J
= 6.63x10-34 Js
= 1.60x1014 s-1

25

Rydberg Equation

• Wavelength emitted by the electron between two
energy levels can be calculated using Rydberg
equation:

1  RH 11
λ 2 n 22
n 1

where

RH = 1.097  107 m-1
 = wavelength

Since  should have a positive value thus n1 < n2

26

Example
Calculate the wavelength, in nanometers of the
spectrum of hydrogen corresponding to n = 2 and
n = 4 in the Rydberg equation.

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Solution:

1 R H 1 1
λ 2 2
n 1 n 2

1  1.097  10 7 m1  1  1 
  22 42 

  4.86  107 m

 4.86  107  109 nm

 486nm

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Exercise:

1) Calculate the energy of hydrogen electron in the:
(a) 1st orbit
(b) 3rd orbit
(b) 8th orbit

2) Calculate the energy change (J), that occurs
when an electron falls from n = 5 to n = 3 energy
level in a hydrogen atom.

3) Calculate the frequency and wavelength (nm) of
the radiation emitted in question 2.

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Answer:

1) Calculate the energy of hydrogen electron in the:

(a) 1st orbit (b) 3rd orbit

E1  RH  1  E1  RH  1 
12 12

  2.18 x 10 18  1   2.18 x 1018  1 
12 32

  2.18 x 1018 J   2.42 x 1019 J

(c) 8th orbit

E1  RH  1 
 12 

 2.18 x 10 18  1 
 82 

  3.41 x 1020 J 30

Answer:

2) Calculate the energy change (J), that occurs
when an electron falls from n = 5 to n = 3
energy level in a hydrogen atom.

E  RH (1  1)
52 32

 2.18 X1018 ( 1  1 )
52 32

  1.55 X 1018 J

31

Answer:

3) Calculate the frequency and wavelength (nm) of
the radiation emitted in question 2.

  h

 1.55 x 10 18 J
6.63 x 1034 Js

  2.34 x 1015 s1

  hc


   6.63 x 1034 Js 3.00 x108 ms1
1.55 x 10 18 J
1.28 x 10-7 m

32

Emission Spectra

i) Continuous ii) Line
Spectra Spectra

Emission and absorption spectra may show a continuous spectrum, a line spectrum or a band spectrum

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i) Continuous Spectrum
• A spectrum consists of radiation with

unbroken sequence of frequencies over a
relatively wide range of wavelength.
• Example : electromagnetic spectrum, rainbow

34

Regions of the Electromagnetic Spectrum
35

FORMATION OF CONTINUOUS SPECTRUM

Continuous spectrum is produced by white light
(sunlight or incandescent lamp) that passed through
a prism

36

ii) Line Spectrum (atomic spectrum)

A spectrum consists of discontinuous or discrete
lines with specific wavelengths and frequencies
in which each line is produced by the transition
of electron between two energy levels.

37

FORMATION OF ATOMIC / LINE SPECTRUM

Spectral lines

prism film

gas discharge tube

• It is composed when the light from a gas discharge
tube containing a particular element is passed
through a prism.

• The emitted light (photons) is then separated into its
components by a prism.

38

• Each component is focused at a definite position,
according to its wavelength and forms as an
image on the film of the photographic plate.

• The images are called spectral lines.

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Example :

• The line emission spectrum of hydrogen atom
• Line spectrum are composed a few wavelengths

giving a series of discrete line separated by blank
areas
• It means each line corresponds to a specific
wavelength and frequency.

line emission spectrum of hydrogen atom

40

FORMATION OF ATOMIC / LINE SPECTRUM

Energy n= • Energy absorbed
n=5 by the atom causes
n=4 the electron
n=3 promoted from a
lower to a higher-
n=2 energy level, ni.

n=1 • The electron is at
excited state (very
unstable) and will
fall to lower energy
level.

41

FORMATION OF ATOMIC / LINE SPECTRUM

Energy n= When the electrons
n=6 fall to lower energy
n=5 levels, nf, photons
n=4 energies are
emitted in the form
n=3 of light with specific
wavelength can be
n=2 detected as a line
spectrum

Emission of photon

42

Line spectrum series

• For the emission line spectra,

nf is the energy level to where the electron falls
ni is the energy level from where the electron falls
• If an electron falls to energy level 1 (nf = 1), it forms Lyman
series.
• If an electron falls to energy level 2 (nf = 2), it forms Balmer
series.
• If an electron falls to energy level 3 (nf = 3), it forms
Paschen series.
• If an electron falls to energy level 4 (nf = 4), it forms
Brackett series.
• If an electron falls to energy level 5 (nf = 5), it forms Pfund
series.

43

Exercise: Complete the following table

Series nf ni Spectrum
region

Lyman 1 2,3,4,… ultraviolet
Balmer 2 3,4,5,… Visible
Paschen 3 4,5,6,… Infrared
Brackett 4 5,6,7,… Infrared
Pfund 5 6,7,8,… Infrared

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n=5 The transition of
electrons to form
n=4 series of spectrum
n=3

n=2

The fall from any excited state to n=2
produces Balmer series

The fall from any excited state to n=1 n=1
produces a line in Lyman series
Balmer series
‫ג‬1

First line in the Balmer series
(Electron falls from n=3 to n=2

FORMATION OF ATOMIC / LINE SPECTRUM

Energy n=
n=5
n=4

n=3

n=2

n=1 Emission of photon

Line spectrum E
of Lyman series 

46

FORMATION OF ATOMIC / LINE SPECTRUM

n=
n=5

n=4

Energy n=3

n=2

n=1

Line E
spectrum 

Lyman Series Balmer Series 47

Emission of photon

Emission series of hydrogen atom

n= Pfund series
n=4
n=3 E4   RH
n=2 42
Brackett series
n=1 Paschen series E3   RH
32

Balmer series E2   RH
22

Lyman series E1   RH
12

48

Example 1

The following diagram is the line spectrum of
hydrogen atom. Line A is the first line of the Lyman
series.

Line A B C DE E
spectrum 



Specify the increasing order of the radiant energy,

frequency and wavelength of the emitted photon.

Which of the line that corresponds to

i) the shortest wavelength? Line E

ii) the lowest frequency? Line A

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Example 2

Line WY
spectrum
Balmer series

State the transitions of electrons that lead to the
lines W, and Y, respectively.

Solution

For W: transition of electron is from n=4 to n=2
For Y: electron shifts from n=7 to n=2

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