CBSE Class 12 Physics 2023 Delhi Set 1 Paper

© examsnet.com
Question : 30
Total: 35
(a) (i) Differentiate between 'distance of closest approach' and 'impact parameter'.
(ii) Determine the distance of closest approach when an alpha particle of kinetic energy 3.95 MeV approaches a nucleus of Z=79, stops and reverses its directions.
OR
(b) (i) State three postulates of Bohr's theory of hydrogen atom.
(ii) Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.
(a) (i) Difference between "distance of closest approach" and "impact parameter":
 Distance of closest approach  Impact Parameter
 Distance of closest approach is the distance of a charged particle from the centre of the nucleus where the total kinetic energy of the charged particle gets converted into potential energy.  Impact parameter is the perpendicular distance between the path of projected charged particles and centre of the nucleus.
  r=
Ze2
4πε0(
1
2
m
v2
)
 b=
Ze2cot(θ2)
4πε0(
1
2
m
v2
)

(ii) Distance of closest approach =r=
Qq
4πε0E

Q=79e=79×1.6×1019C
q=2e=2×1.6×1019C
E=3.95MeV
=3.95×106×1.6×1019J
r=(9×109)
(79×1.6×1019)×(2×1.6×1019)
3.95×106×1.6×1019

=576×1016m
=5.76×1014m
OR
(b) (i) Postulates of Bohr's theory:

Postulate 1: In an atom electrons are revolving around the nucleus in definite circular orbits. These orbits are called 'stationary orbits' and each orbit or shell possesses fixed energy. While revolving in these orbits electrons do not emit any radiation.

Postulate 2: Electrons can move only those permissible orbits where the angular momenta of electrons are integral multiples of
h
2π
where h is the
Planck's constant.
Postulate 3: Transition of electrons may occur from one stationary orbit to another. During such transition energy may be emitted or absorbed following the relation EiEf=hv (where EiEf is the difference of energies of the two stable orbits).
(ii) Angular momentum of electron revolving in 2nd orbit in Bohr's Hydrogen atom:
Angular momentum =
nh
2π

Here, n=2,
Angular momentum =2×
h
2π
=
h
π
© examsnet.com
Go to Question: