A particle is moving 3 times faster than the speed of electron. If the ratio of wavelength of partic

Question

A particle is moving 3 times faster than the speed of electron. If the ratio of wavelength of particle and electron is $1.8 	imes 10^{-4}$, then particle is\

Professor PC Thomas Classes · Answer

(a) : Given : $\frac{\lambda_{	ext {particle }}}{\lambda_{	ext {electron }}}=1.8 	imes 10^{-4}$ and $\frac{v_{	ext {particle }}}{v_{	ext {electron }}}=3$ 
According to de Broglie equation, $\lambda=\frac{h}{m v}$ 
$ \begin{aligned} \frac{\lambda_{	ext {particle }}}{\lambda_{	ext {electron }}} & =\frac{h}{m_{	ext {particle }} 	imes v_{	ext {particle }}} 	imes \frac{m_{	ext {electron }} 	imes v_{	ext {electron }}}{h} \ & =\frac{m_{	ext {electron }}}{m_{	ext {particle }}} 	imes \frac{v_{	ext {electron }}}{v_{	ext {particle }}} \ \Rightarrow \quad 1.8 	imes 10^{-4} & =\frac{9.1 	imes 10^{-31} \mathrm{~kg}}{m_{	ext {particle }}} 	imes \frac{1}{3} \ m_{	ext {particle }} & =\frac{9.1 	imes 10^{-31}}{1.8 	imes 10^{-4} 	imes 3}=1.6852 	imes 10^{-27} \mathrm{~kg} \end{aligned} $ 
Actual mass of neutron is $1.67493 	imes 10^{-27} \mathrm{~kg}$.\ Hence, the particle is neutron.\