Q. If helium atom and hydrogen molecules are moving with the same velocity, their wavelength ratio will be
A) $4:1$
B) $1:2$
C) $2:1$
D) $1:4$
Explanation
(b)
According to de-Broglie,
$\lambda = \frac{h}{mv}$
or $\frac{\lambda_{He}}{\lambda_{H_{2}}} = \frac{m_{H_{2}}}{m_{He}} \times \frac{v_{H_{2}}}{v_{H_{e}}}$
Given, $v_{H_{2}} = v_{He}$
$\therefore\ \ \ \ \ \ \ \ \ \frac{\lambda_{He}}{\lambda_{H_{2}}} = \frac{2}{4} \times \frac{v_{He}}{v_{He}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.