Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
2922 Upvotes
Verified Answer
The correct answer is:
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.
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.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.