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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 3.95MeV 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.
(ii) Determine the distance of closest approach when an alpha particle of kinetic energy 3.95
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.
Solution: 👈: Video Solution
(a) (i) Difference between "distance of closest approach" and "impact parameter":
(ii) Distance of closest approach= r =
Q = 79 e = 79 × 1.6 × 10 − 19 C
q = 2 e = 2 × 1.6 × 10 − 19 C
E = 3.95 MeV
= 3.95 × 10 6 × 1.6 × 10 − 19 J
∴ r = ( 9 × 10 9 )
= 576 × 10 − 16 m
= 5.76 × 10 − 14 m
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
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 relationE i − E f = h v (where E i ∼ E f is the difference of energies of the two stable orbits).
(ii) Angular momentum of electron revolving in2 nd orbit in Bohr's Hydrogen atom:
Angular momentum=
Here,n = 2 ,
∴ Angular momentum = 2 ×
=
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. | ||||||||
| |
(ii) Distance of closest approach
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
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
(ii) Angular momentum of electron revolving in
Angular momentum
Here,
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