Question

The de-Broglie wavelength of a neutron at $27^{\circ }C$ is $\lambda$. What will be its wavelength at $927^{\circ }C$

• A. $\lambda /2$
• B. $\lambda /3$
• C. $\lambda /4$
• D. $\lambda /9$

Answer 1

Answer: (A)

${\lambda }_{\text{neutron }}\propto \frac{1}{\sqrt{T}}$
$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{T_2}{T_1}}$
$\Rightarrow \frac{\lambda }{{\lambda }_2}=\sqrt{\frac{(273+927)}{(273+27)}}$
$=\sqrt{\frac{1200}{300}}=2$
$\Rightarrow {\lambda }_2=\frac{\lambda }{2}$