Download Bohr`s model of atom- postulates The electron in an atom moves

Bohr’s model of atom- postulates

The electron in an atom moves around the nucleus in a circular path of fixed energy called orbits

or stationary states, or energy states.
Energy is absorbed when electron jumps from lower orbit to a higher orbit and is emitted when

electron jumps from higher orbit to a lower orbit.
Bohr frequency rule: Frequency ( ) of absorbed or emitted radiation is given by,
Where, E1 and E2 are the energies of lower and higher allowed energy
states respectively
 Angular momentum (L) of an electron in a stationary state is given by,

Energy of a stationary state for H-atom is given by
En =
- 2. 18 x 10-18 J
n2.
2.18 x 10 -18 J is also called Rydberg constant

The energy of the lowest energy state (n =1) is

For Hydrogen like species (He +, Li2+, Be 3+)
En = - 2. 18 x 10-18 x Z2 J
E 1 = - 2. 18 x 10 -18 J
n2

Radii of the orbit,
rn = 52. 9 x n2
Z

pm
, where Z is the atomic no:
Energy of transition of electrons
∆ E = E f - E i = - 2 .18 x 10 -18( 1 - 1 )
nf2 ni2
∆ E = 2 .18 x 10 -18 ( 1 - 1 ) J
ni2
nf2
 For absorption spectrum, n f > n i , ∆E is + ve, energy is absorbed.
 For emission spectrum, n i > n f , ∆E is -ve, energy is released.
Q. Why is electronic energy negative?
When the e- is free from the influence of nucleus (n=∞ ), the energy is taken as zero. When the eis attracted by the nucleus, energy is emitted, and the energy is lowered and becomes negative
value.
Problem 2.10(page no45)
Problem2.11
Limitations of Bohr’s Model of Atom

Unable to explain the spectrum of multi-electron atoms (For example − helium atom

which contains two electrons)
Unable to explain splitting of spectral lines in electric field (Stark effect) or in magnetic

field (Zeeman effect)
Unable to explain the fine spectral lines in H atom.

It failed to explain about the ability of atom to form molecules by chemical bonds.
Dual Behaviour of Matter

Matter, like radiation, exhibits dual behaviour (i.e., both particle and wave-like
properties).
de Broglie Equation
Give the relationship between wavelength (λ) and momentum (p) of a material particle.
Where, m is the mass of the particle and v is its velocity



According to de Broglie, every object in motion has a wave character.
Wavelengths of objects having large masses are so short that their wave properties cannot
be detected.
Wavelengths of particles having very small masses (electron and other subatomic
particles) can be detected experimentally.
Q. Why don’t we observe the wave properties of large objects like cricket ball?
Because of their large mass, wavelength is small,hence cannot be detected.
Problem2.12(page 47)
Problem2.13
Problem2.14
Heisenberg’s Uncertainty Principle
It is impossible to determine simultaneously the exact position and exact momentum of an
electron (microscopic particle) with absolute accuracy and certainty

Mathematically, it can be represented as
Δx × Δp ≥
Or, Δx ×m Δv ≥
Where Δx is the uncertainty in position, Δv is the uncertainty in
velocity, Δp is the uncertainty in momentum
Significance of Uncertainty Principle

Heisenberg’s uncertainty principle rejects the existence of definite paths or trajectories of
electrons and other similar particles.(orbit is replaced by orbital)
Heisenberg’s uncertainty principle is significant only for the motion of microscopic
objects and is negligible for macroscopic objects.

Reasons for the failure of the Bohr Model

Bohr model ignores the dual behaviour of matter − It does not account for the wave
character of an electron.
Bohr model ignores Heisenberg’s uncertainty Principle

Q. What is the difference between orbit and orbital?
Orbit
Orbital
1. Circular path around the nucleus in which
electrons revolve.
1. It is the region of space around the nucleus
where the probability of finding the electron
is maximum.
2.Two dimensional
2.Three dimensional
3. An orbit can accommodate a max. of
2n2 e-s
3. An orbital can accommodate a max. of
2 e-s
4.It is against Heisenberg’s uncertainty
principle
4.It is in accordance with Heisenberg’s
uncertainty principle
5.Circular shape
5.Different shapes
6.Non-directional
6.Directional except s-orbital
Problem 2.15(page 49)
Problem2.16
Quantum numbers:
(i) Principal quantum number (n)
(ii) Azimuthal quantum number (l)
(iii) Magnetic quantum number (ml) (iv) Spin quantum number (ms )


An orbital is designated by 3 quantum nos.-n, l, ml
An electrons designated by 4 quantum nos.-n, l , ml ,ms
1. The principal quantum number (n)
o
o
o
Identifies the shell (n = 1, 2, 3,………)
Determines the size and energy of the orbital
With an increase in the value of n, there is an increase in the number of allowed
orbitals (n2), the size of an orbital and the energy of an orbital.
2. The Azimuthal quantum number (l)
a. Also known as orbital angular momentum or subsidiary quantum number
b. Identifies subshells and shapes of the orbital
c. l can have values, ranging from 0 to n − 1.
d. For n = 1, l = 0
[1s subshell]
For n = 2, l = 0, 1
[2s, 2p subshell]
For n = 3, l = 0, 1, 2 [3s, 3p, 3d subshell]
For n = 4, l = 0, 1, 2, 3, [4s, 4p,4d, 4f subshell ]………and so on
e. Each shell consists of one or more sub-shells or sub-levels.
Value for l
0
1
2
3
4
5 ……
Notation for sub-shell
s
p
d
f
g
h ……
Principal quantum number (n)
Azimuthal quantum number (l)
Sub-shell notations
1
0
1s
2
0
2s
2
1
2p
3
0
3s
3
1
3p
3
2
3d
4
0
4s
4
1
4p
4
2
4d
4
3
4f
3. The magnetic quantum number (ml):
a. Gives information about orientation of the orbital and no. of orbitals.
b. Total ml values = 2l + 1.
ml = −l to l
Example:
For l = 0, ml = 0 (one s-orbital)
For l = 1, ml = −1, 0 + 1 (three p-orbitals)
For l = 2, ml = −2, −1, 0, +1, +2 (five d-orbitals)
For l = 3, ml = −3, −2, −1, 0, + 1, +2, + 3 (seven f-orbitals)
Sub-shell notation
Number of orbitals
Max. electrons
s
p
d
f
1
3
5
7
2
6
10
14
4. Spin quantum number (ms).
o
It designates the spin of an electron. There are two orientations or two spin states
o
of an electron: + and − or ↑(spin up) and ↓(spin down)
An orbital cannot hold more than two electrons.
Boundary Surface Diagrams
Boundary surface diagrams for 1s and 2s orbitals are:
o
Boundary Surface Diagrams: 1s and 2s are spherical in shape.

Boundary surface diagram for three 2p orbitals (l = 1) are shown in the figure below.

Boundary diagrams for the five 3d orbitals are shown in the figure below.

Nodes
The region where the probability of finding the electron is zero is called nodal surface or
node.
The total number of nodes is given by (n-1) i.e, sum of l angular nodes and (n-l-1) radial
nodes.
Radial node: are nodes present along the axis.
Angular node: are nodes at the plane bisecting the lobes passing through the nucleus
Total node = n-1; Radial node = n-l-1 ; Angular node = l
Eg: 2p
n=2;
l=1
Total node = n-1=2-1=1;
Energy of Orbitals:
Radial node = n-l-1=2-1-1=0 ;
Angular node = l =1
Shieding effect: It is the shielding of outer electrons from the nucleus by the inner electrons.
Effective nuclear charge (Z eff): The net + ve charge experienced by the e- from the nucleus.
The order of eff.nuclear charge: s> p > d
n + l Rule
 Lower the value of (n + l) for an orbital, lower is its energy.
 When two orbitals have the same value of (n + l), the orbital with lower value of n
will have lower energy.
Filling of Orbitals in Atom & Electronic Configuration of Atoms
1. Aufbau Principle
In the ground state of atoms, the orbitals are filled in the increasing order of their
energy.

The given table shows the arrangement of orbitals with increasing energy on the basis of
(n + l) rule.
Value of
Orbitals
Value of n
Value of l
(n +1)
1s
1
0
1+0=1
2s
2
0
2+0=2
2p
2
1
2+1=3
2p (n = 2) has lower energy than 3s
3s
3
0
3+0=3
3s (n = 3)
3p
3
1
3+1=4
3p (n = 3) has lower energy than 4s
4s
4
0
4+0=4
4s (n = 4)
3d
3
2
3+2=5
3d (n = 3) has lower energy than 4p
4p
4
1
4+1=5
4p (n = 4)
Increasing order of the energy of the orbitals and hence, the order of the filling of orbitals: 1s, 2s,
2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s, …
2. Pauli Exclusion Principle
No two electrons in an atom can have the same set of four quantum numbers. (Or)
Only two electrons may exist in the same orbital and these orbitals must have opposite spin.

The maximum number of electrons in the shell with the principal quantum number n is
equal to 2n2.
3. Hund’s Rule of Maximum Multiplicity
Pairing of electrons in the orbitals of same sub-shell (p, d, or f) does not take place until
each orbital has got one electron each (i.e., singly occupied).

Orbitals of equal energy (i.e., same sub-shell) are called degenerate orbitals.
Electronic Configuration of Atom For example
Stability of completely filled and half-filled sub-shells is due to
(i) Symmetrical Distribution of Electrons. (ii) High exchange energy
SAMPLE QUESTIONS
1. What is black body radiation?
2. Explain Plancks quantum theory?
3. What is photoelectric effect? explain
4. What is work function?
5. Define the following terms: (a)
11. Write the difference between orbit
Emission spectra (b)Absorption
spectra
and orbital ?
12. What is radial node and spherical
6. Explain hydrogen spectra?
node? How many nodded possible
7. Describe Bohrs model of atom ?
for 2 p orbital.
Mention its limitations .
13. State the following (a) Aufbau
8. What are stark and Zeeman effect ?
principle (b) Paulis exclusion
9. State the following
principle (c) Hunds rule (d)n+l rule
a.de Broglie dual nature of electron
14. Show that circumference of the
b.Heisenberg uncertainty principle.
10. What are the significance of
Heisenberg uncertainty principle ?
Bohr’s orbit for hydrogen atom is an
integral multiple of de Broglie
wave length
Quantum numbers and electronic configuration :
1.Write the electronic configuration of Cu-29 and Cr-24.
2.Write the quantum numbers of the valence electron in Na( z=11) in the ground state
3.Which of the following orbital has highest energy.
(a).n=3 , l=2 ml=+1 (b).n=4 l=0 , ml=0
4.How many unpaired electrons are there in Ni+2?
5.How many electrons in an atom may have the following quantum numbers. (a). n=4 ms=-1/2
(b)n=3 , ml=0
6.An electron is one of the 3d orbital ,Give possible values of n and l.
7.Write the values of azimuthl quantum number(l) for the orbital 4f and 5 p.
8.Which atom are indicated by the follwing electronic configuration .
(a)[He]2S1 (b)[Ne] 3S2 3P3
9.Arrange the following orbital in the order in which they may get filled. 3d,4s,4p,5s,4f.
10.What are the atomic numbers of the elements whose outer most electrons are represented by
(1). 3s1 (2). 2p3 (3).3p5
11.Using s,p,d,f notation ,describe the orbital with the following quantum numbers.
(i) n=2, l=1 (ii) n=4, l= 0 (iii) n=5, l=3
12.The principle quantum number is n=3.
(a)Find no of orbital associated with it (b)Find no of electrons present in it.
13.Arrange the pair of orbital which experiences the larger effective nuclear charge. (a).2s,3s
(b).4d, 4f
14.The unpaired electron is Al and Si are present in 3p orbital. Which electron will experience
more effective nuclear charge?
Numericals in atomic structure
1.The wavelength range of the visible spectrum extends from violet (400 nm) to red (750 nm). Express
these wavelengths in frequencies (Hz). (1nm = 10–9 m)
2.Calculate energy of one mole of photons of radiation whose frequency is 5x1014 Hz.
3.What are the frequency and wavelength of a photon emitted during a transition from n = 5 state to the n
= 2 state in the hydrogen atom?
4.Calculate the energy associated with the first orbit of He+ . What is the radius of this orbit?
5.What will be the wavelength of a ball of mass 0.1 kg moving with a velocity of 10 m s–1 ?
6.The mass of an electron is 9.1x10-31 kg. If its K.E. is 3.0x10 -25 J, calculate its wavelength.
7.Calculate the mass of a photon with wavelength 3.6 Å.
8.A microscope using suitable photons is employed to locate an electron in an atom within a distance of
0.1 Å. What is the uncertainty involved in the measurement of its velocity?
9.A golf ball has a mass of 40g, and a speed of 45 m/s. If the speed can be measured within accuracy of
2%, calculate the uncertainty in the position.
10.Find energy of each of the photons which (i) correspond to light of frequency 3×1015 Hz.
(ii) have wavelength of 0.50 Å.
11.What is the number of photons of light with a wavelength of 4000 pm that provide 1J of energy?
12.What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition
from an energy level with n = 4 to an energy level with n = 2?.
13.What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops
to the ground state?
14.The electron energy in hydrogen atom is given by En = (–2.18 x10–18 )/n2 J. Calculate the energy
required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in
cm that can be used to cause this transition?