A particle is moving 3 times faster than the speed of electron. If...

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

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A. neutron

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.