Question

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

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

Answer 1

The correct option is A $\lambda /2$

${\lambda }_{neutron}\propto \frac{1}{\sqrt{T}}\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{T_2}{T_1}}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{(273+927)}{(273+27)}}=2\Rightarrow {\lambda }_2=\frac{\lambda }{2}$