The wavelength of an electron and a neutron will become equal when the velocity of the electron is $x$ times the velocity of neutron. The value of $x$ is ____________. (Nearest Integer)
(Mass of electron is $9.1 \times 10^{-31} \mathrm{~kg}$ and mass of neutron is $1.6 \times 10^{-27} \mathrm{~kg}$ )
Answer (integer)
1758
Solution
$$\lambda_{e}=\frac{h}{m_{e} \times V_{e}}, \quad \lambda_{N}=\frac{h}{m_{N} \times V_{N}}$$
<br/><br/>
$\lambda_{e}=\lambda_{N}$ When $V_{e}=x V_{N}$
<br/><br/>
$\frac{1}{m_{e} V_{e}}=\frac{1}{m_{N} \times V_{N}}$
<br/><br/>
$\frac{m_{N}}{m_{e}}=\frac{V_{e}}{V_{N}}=x$
<br/><br/>
$x=\frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}$
<br/><br/>
$=0.17582 \times 10^{4}$
<br/><br/>
$\simeq 1758$
About this question
Subject: Chemistry · Chapter: Atomic Structure · Topic: Bohr's Model
This question is part of PrepWiser's free JEE Main question bank. 122 more solved questions on Atomic Structure are available — start with the harder ones if your accuracy is >70%.