A particle is travelling 4 times as fast as an electron.

Question:

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is $2: 1$, the mass of the particle is :-

  1. $\frac{1}{16}$ times the mass of $\mathrm{e}^{-}$

  2. 8 times the mass of $e^{-}$

  3. 16 times the mass of $\mathrm{e}^{-}$

  4. $\frac{1}{8}$ times the mass of $\mathrm{e}^{-}$


Correct Option: , 4

Solution:

$\lambda=\frac{\mathrm{h}}{\mathrm{p}}$

$\frac{\lambda_{p}}{\lambda_{e}}=\frac{p_{c}}{p_{p}}=\frac{m_{e} v_{e}}{m_{p} v_{p}}$

$2=\frac{m_{e}}{m_{p}}\left(\frac{v_{e}}{4 v_{e}}\right)$

$\therefore \mathrm{m}_{\mathrm{p}}=\frac{\mathrm{m}_{\mathrm{e}}}{8}$

Leave a comment