Atomic Structure Question 423
Question: The velocity of particle A is $ 0.1m{s^{-1}} $ and that of particle B is $ ~0.05,m{s^{-1}} $ . If the mass of particle B is five times that of particle A, then the ratio of de- Broglie wavelengths associated with the particles A and B is
Options:
A) 2 : 5
B) 3 : 4
C) 6 : 4
D) 5 : 2
Show Answer
Answer:
Correct Answer: D
Solution:
- Given, $ v_{A}=0.1m{s^{-1}} $ and $ v_{B}=0.05m{s^{-1}} $ ms-1 also, $ m_{B}=5m_{A} $ de-Broglie wavelength, $ \lambda =\frac{h}{mv} $
$ \therefore \frac{{\lambda_{A}}}{{\lambda_{B}}}=\frac{h/m_{A}v_{A}}{h/m_{B}v_{B}}=\frac{m_{B}v_{B}}{m_{A}v_{A}} $
$ =\frac{5m_{A}\times 0.05}{m_{A}\times 0.1}=5\times 0.5=2.5=5\text{/}2 $
$ \therefore {\lambda_{A}}:{\lambda_{B}}=5:2 $
