Dual Nature of Radiation and Matter - Result Question 5
5. The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass $m$, is :-[2017]
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======= ####5. The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass $m$, is :-[2017]
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) $\frac{h}{\sqrt{3 mkT}}$
(b) $\frac{2 h}{\sqrt{3 mkT}}$
(c) $\frac{2 h}{\sqrt{mkT}}$
(d) $\frac{h}{\sqrt{mkT}}$
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Answer:
Correct Answer: 5. (a)
Solution:
- (a) We know that,
de-Broglie wavelength $\lambda=\frac{\hbar}{p}=\frac{h}{\sqrt{2 m(KE)}}$
K.E. of thermal neutron $=\frac{3}{2} kT$
$=\frac{h}{\sqrt{2 m(\frac{3}{2} k T)}}$
$\lambda=\frac{h}{\sqrt{3 mkT}}$
