Question

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

• A. $\frac{\lambda }{2}$
• B. $\frac{\lambda }{3}$
• C. $\frac{\lambda }{4}$
• D. $\frac{\lambda }{9}$

Answer 1

The correct option is A

$\frac{\lambda }{2}$

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