Question 159: Dual Nature of Matter and Radiation

Question

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength
of nitrogen molecule is close to :
(Given : nitrogen molecule weight : 4.64 $$ 	imes $$ 10
–26
kg,
Boltzman
constant: 1.38 $$ 	imes $$ 10
–23
J/K,
Planck constant : 6.63 $$ 	imes $$ 10
–34
J.s)

Accepted Answer

We know, the de-Broglie
wavelength
$$\lambda $$ = $${h \over {m{v_{rms}}}}$$
also V
rms
= $$\sqrt {{{3kT} \over m}} $$
$$ 	herefore $$ $$\lambda $$ = $${h \over {\sqrt {3mkT} }}$$
= $${{6.63 	imes {{10}^{ - 34}}} \over {\sqrt {3 	imes 4.6 	imes {{10}^{ - 26}} 	imes 1.38 	imes {{10}^{ - 23}} 	imes 400} }}$$
= 2.4 $$ 	imes $$ 10
-11
m
= 0.24 $$\mathop A\limits^o $$

Answer

0.44 $$\mathop A\limits^o $$

Answer

0.34 $$\mathop A\limits^o $$

Answer

0.20 $$\mathop A\limits^o $$

Answer

0.24 $$\mathop A\limits^o $$

Dual Nature of Matter and Radiation

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64 $ \times 10 –26 kg, Boltzman constant: 1.38 \times 10 –23 J/K, Planck constant : 6.63 \times $ 10 –34 J.s)

Choose the correct answer: