Q. A particle $A$ moving with a certain velocity has the de-Broglie wavelength of 1 $A{^\circ}$. For particle $B$ with mass 25% of $A$ and velocity 75% of $A$, calculate the de-Broglie wavelength
A) $3\ A{^\circ}$
B) 5.33$\ A{^\circ}$
C) 6.88$\ A{^\circ}$
D) 0.48$\ A{^\circ}$
Explanation
(b)
$\lambda_{A} = \frac{h}{m_{A}v_{A}}$ and $\lambda_{B} = \frac{h}{m_{B}v_{B}}$
$\frac{\lambda_{A}}{\lambda_{B}} = \frac{m_{B}v_{B}}{m_{A}v_{A}}$
$\frac{1 \times 10^{- 10}}{\lambda_{B}} = \frac{m_{A} \times 3v_{A}}{m_{A} \times 4 \times v_{A} \times 4}$
$\lambda_{B} = \frac{16 \times 10^{- 10}}{3} = 5.33\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.