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. (1) $\frac{1}{16}$ times the mass of e-

2. (2) 8 times the mass of $\mathrm{e}^{-}$

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

4. (4) $\frac{1}{8}$ times the mass of e-

Correct Option: , 4

Solution:

(4)

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

$\frac{\lambda_{\mathrm{p}}}{\lambda_{\mathrm{e}}}=\frac{\mathrm{P}_{\mathrm{e}}}{\mathrm{P}_{\mathrm{p}}}=\frac{\mathrm{m}_{\mathrm{e}} \mathrm{v}_{\mathrm{e}}}{\mathrm{m}_{\mathrm{p}} \mathrm{v}_{\mathrm{p}}}$

$2=\frac{\mathrm{m}_{\mathrm{e}}}{\mathrm{m}_{\mathrm{p}}}\left(\frac{\mathrm{v}_{\mathrm{e}}}{4 \mathrm{v}_{\mathrm{e}}}\right)$

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