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

• A. $4.8\times {10}^{-27}\text{kg}$
• B. $9.1\times {10}^{-31}\text{kg}$
• C. $1.2\times {10}^{-28}\text{kg}$
• D. $9.7\times {10}^{-28}\text{kg}$

Answer 1

The correct option is D $9.7\times {10}^{-28}\text{kg}$

de Broglie wavelength

$\lambda =\frac{h}{mv}\Rightarrow m=\frac{h}{\lambda v}$

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
$\Rightarrow \frac{m^{\prime }}{m}=\frac{v\lambda }{v^{\prime }{\lambda }^{\prime }}=\frac{1}{5}\times \frac{1}{1.878\times {10}^{-4}}$
$m^{\prime }=\frac{1}{5}\times \frac{1}{1.878\times {10}^{-4}}\times 9.1\times {10}^{-31}$

$\Rightarrow m=9.7\times {10}^{-28}\text{kg}$