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

Smart Achievers · Accepted Answer

(4)

Given: $v_{p a r t i c l e} = 4 v_{e l e c t r o n}$ and $λ_{p a r t i c l e} \times 2 λ_{e l e c t r o n}$

Using $λ = \frac{h}{p}$

$λ P = c o n s t a n t$

$∴$ $λ_{p a r t i c l e} \times p_{p a r t i c l e} = λ_{e l e c t r o n} \times p_{e l e c t r o n}$

$\Rightarrow λ_{p a r t i c l e} \times m_{p a r t i c l e} \times v_{p a r t i c l e}$

$= λ_{e l e c t r o n} \times m_{e l e c t r o n} \times v_{e l e c t r o n}$

$∴$ $m_{p a r t i c l e} v_{p a r t i c l e} = \frac{m_{e l e c t r o n} v_{e l e c t r o n}}{2}$

$\Rightarrow m_{p a r t i c l e} = \frac{m_{e l e c t r o n}}{8}$

Solution

Q.
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 16 times the mass of $e^{-}$

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

3 $\frac{1}{16}$ times the mass of $e^{-}$

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

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Solution

Q. 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 16 times the mass of e-

2 8 times the mass of e-

3 116 times the mass of e-

4 18 times the mass of e-