JEE Main Solved Paper 2017 Question 24
Question: A particle A of mass m and initial velocity v collides with a particle B of mass $ \frac{m}{2} $ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $ {\lambda_A} $ to $ {\lambda_B} $ after the collision is: [JEE Main Solved Paper-2017]
Options:
A) $ \frac{{\lambda_A}}{{\lambda_B}}=\frac{2}{3} $
B) $ \frac{{\lambda_A}}{{\lambda_B}}=\frac{1}{3} $
C) $ \frac{{\lambda_A}}{{\lambda_B}}=\frac{1}{3} $
D) $ \frac{{\lambda_A}}{{\lambda _{ _{B}}}}=2 $
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Answer:
Correct Answer: D
Solution:
- By conservation of linear momentum $ mv=mv _1+\frac{m}{2}v _2 $ $ 2v=2v _1+v _2 $ ?. by law of collision $ e=\frac{v _2-v _1}{u _1-u _2} $ $ u=v _2-v _1 $ ?. By equation [a] and [b] $ v _1=\frac{v}{3}; $ $ v _2=\frac{4v}{3} $ $ {\lambda_1}=\frac{h}{p _1}; $ $ {\lambda_2}=\frac{h}{o _2} $ $ \frac{{\lambda_1}}{{\lambda_2}}=\frac{2}{1} $ Option [d]
