Question:
A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878 \times 10^{-4}$. The mass of the particle is close to :
Correct Option: , 4
Solution:
(4)
de Broglie wavelength
$\lambda=\frac{h}{m v} \Rightarrow m=\frac{h}{\lambda v}$
Clearly, $m \propto \frac{1}{\lambda v}$
If $\lambda$ and $v$ be the wavelength and velocity of electron and $\lambda^{\prime}$ and $v^{\prime}$ be the wavelength and velocity of the particle then
$\Rightarrow \frac{m^{\prime}}{m}=\frac{v \lambda}{v^{\prime} \lambda^{\prime}}=\frac{1}{5} \times \frac{1}{1.878} \times 10^{-4}$
$\Rightarrow m=9.7 \times 10^{-28} \mathrm{~kg}$