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




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

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

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

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