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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
Questions With Solutions

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Question : 17
Total: 37
(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
 kT at 300 K.
Solution:  
(a) de Broglie wavelength, λ =
h
√2mK
∴ Kinetic energy (K) of neutron
K =
h2
2mλ2
 =
(6.63×10−34)2
2×1.677×10−27×(1.40×10−10)2
= 6.686 × 10−21 J
=
6.686×10−21
1.6×10−19
 eV = 4.178 × 10−2 eV
(b) K =
3
2
 kT, where k = Boltzmann constant
∴ λ =
h
√2mK
 =
h
√3mkT
=
6.63×10−34
√3×1.677×10−27×1.38×10−23×300
m =
6.63×10−10
√20.8
 =
6.63×10−10
4.56
 m = 1.45 × 10−10 = 0.145 nm
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