11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10–10 m?
(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.
11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10–10 m?
(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.
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1 Answer
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11.17 De Broglie wavelength of the neutron, = 1.40 m
Mass of neutron, m = 1.66 kg
Planck’s constant, h = 6.626 Js
Kinetic energy, = ………….(1)
De Broglie wavelength and velocity (v) are related as
…………….(2)
Combining equation (1) and (2), we get
= = = = 6.75 J = eV = 42.17
Temperature of the neutron, T = 300 K
Average kinetic energy of the neutron, = ,
where k = Boltzmann constant = 1.38 kg
= &n
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Based on theory
z² × (13.6) (1 - ¼) = 3 × (13.6)
z = 2 . (i)
h/√2mk? = (1/2.3) × h/√2mk?
=> k? = (2.3)²k? = 5.25k? (ii)
Now, k? = E? - Φ
k? = E? - Φ = z²E? - Φ
∴ k? /k? = (10.2 - Φ)/ (4 × 10.2 - Φ) = 1/5.25
=> Φ = 3eV
- (i)
- (ii)
from (i) & (ii)
ev
hu = hu0 + K.E
Cases u = 2u0
h2u0 = hu0 + K.E1
K.E1 = hu0
- (1)
Now, cases 2
h 5u0 = hu0 + k.E2
k.E2 = 4hu0
v2 =
v2 = 2v1
This is a Short Answer Type Questions as classified in NCERT Exemplar
Sol:
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