Q. If $E_{e},E_{a}$ and $E_{p}$ represent the kinetic energies of an electron, alpha particle and a proton respectively, each moving with same de-Broglie wavelength then
A) $E_{e} = E_{\alpha} = E_{p}$
B) $E_{e} > E_{\alpha} > E_{p}$
C) $E_{\alpha} > E_{p} > E_{e}$
D) $E_{e} > E_{p} > E_{\alpha}$
Explanation
(d)
$\lambda = \frac{h}{mv}\ \ \ \ \ \lbrack mv = \sqrt{2m \bullet KE}\rbrack$
$\lambda = \frac{h}{\sqrt{2m \bullet KE}}$
$KE \propto \frac{1}{\lambda^{2}\sqrt{2m}}$
Since, $\lambda\$is same,
$KE \propto \frac{1}{m}$
The order of mass of electron, alpha particle and proton is $m_{a} > m_{p} > m_{e}$
Thus, the order of KE is $E_{e} > E_{p} > E_{a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.