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

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Question : 19
Total: 37
What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-mean-square speed of molecules at this temperature.
(Atomic mass of nitrogen = 14.0076 u, K = 1.38 × 10–23JK–1).
Solution:  
Let us first calculate mass of each N2 molecule.
m = 2 × 14. 0076 × 1.66 × 10–27 kg = 46.5 × 10–27 kg
T = 300 K
Average kinetic energy of N2 molecules at temperature T
1
2
mvmax2 =
3
2
 kT or vrms = √
3kT
m
∴ λ =
h
mvrms
 =
h
√3mkT
=
6.63×10−34
√3×46.5×10−27×1.38×10−23×300
m
=
6.63×10−34
√577.53×10−24
 =
6.63×10−10
24.03
 m = 0.0276 × 10−19 m = 0.028 nm
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