Question

An electron of a velocity $x$ is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is:

• A. $\frac{x}{1840}$
• B. $\frac{x}{920}$
• C. $3680x$
• D. $\frac{x}{3680}$

Answer 1

Answer: (B)

$\frac{x}{920}$

$\lambda =\frac{h}{m_{e}v}[v=x]$

Let the velocity of neutron be Y,

$\frac{\lambda }{2}=\frac{h}{m_{n}Y}$

$\frac{2h}{m_{n}Y}=\frac{h}{m_{e}x}\Rightarrow \frac{m_{n}Y}{2}=m_{e}x$

$Y=\frac{2m_{e}x}{m_n}$

$Y=\frac{x}{920}$
Option B is correct.