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A particle of mass

Question:

A particle of mass $4 \mathrm{M}$ at rest disintegrates into two particles of mass $\mathrm{M}$ and $3 \mathrm{M}$ respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass $M$ to that of mass $3 \mathrm{M}$ will be:

1. $1: 3$

2. $3: 1$

3. $1: \sqrt{3}$

4. $1: 1$

Correct Option: , 4

Solution:

$\lambda=\frac{h}{p}$

both the particles will move with momentum same in magnitude \& opposite in direction.

So De-Broglie wavelength of both will be same i.e. ratio $1: 1$