Q. An electron and a proton have the same de-Broglie wavelength. Then the kinetic energy of the electron is
A) Zero
B) Infinity
C) Equal to kinetic energy of the proton
D) Greater than the kinetic energy of proton
Explanation
(d) As $E_{K} = \frac{1}{2}mv^{2}$ or $mv = \sqrt{2m\ E_{K}}$
As per question;
or $m_{p}v_{p} = m_{e}v_{e}$
or $\sqrt{2m_{p}\ {E_{K}}_{p}} = \sqrt{2m_{e}\ {E_{K}}_{e}}$
or $\frac{{E_{K}}_{e}}{{E_{K}}_{p}} = \frac{m_{p}}{m_{e}} > 1$
or ${E_{K}}_{e} > {E_{K}}_{p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.