Q35 / 180 · AIIMS 2013 · Chemistry

A particle is moving 3 times faster than the speed of electron. If the ratio of wavelength of particle and electron is $1.8 \times 10^{-4}$, then particle is

  • Correct answer
    A
    neutron
  • B
    $\alpha$-particle
  • C
    deuteron
  • D
    tritium

Solution

Given $: \frac{\lambda_{\text {particle }}}{\lambda_{\text {electron }}}=1.8 \times 10^{-4}$ and $\frac{v_{\text {particle }}}{v_{\text {electron }}}=3$ According to de-Broglie equation, $\lambda=\frac{h}{m v}$ $\frac{\lambda_{\text {particle }}}{\lambda_{\text {electron }}}=\frac{h}{m_{\text {particle }} \times v_{\text {particle }}} \times \frac{m_{\text {electron }} \times v_{\text {electron }}}{h}$ $=\frac{m_{\text {electron }}}{m_{\text {particle }}} \times \frac{v_{\text {electron }}}{v_{\text {particle }}}$ $\Rightarrow 1.8 \times 10^{-4}=\frac{9.1 \times 10^{-31} \mathrm{~kg}}{m_{\text {particle }}} \times \frac{1}{3}$ $m_{\text {particle }}=\frac{9.1 \times 10^{-31}}{1.8 \times 10^{-4} \times 3}$ $=1.6852 \times 10^{-27} \mathrm{~kg}$ Actual mass of neutron is $1.67493 \times 10^{-27} \mathrm{~kg}$. Hence, the particle is neutron.

Hence, the correct answer is option: 'A'.

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