Question

A particle of mass $4M$, initially at rest, disintegrates into two particles of masses $M$ and $3M$, respectively, having non-zero velocities. The ratio of de-Broglie wavelength of the particle of mass $M$, to that of mass $3M$, will be,

• A. $3:1$
• B. $1:1$
• C. $1:\sqrt{3}$
• D. $1:3$

Answer 1

The correct option is B $1:1$

The de-Broglie wavelength is given by,
$\lambda =\frac{h}{p}$
According to conservation of momentum principle, the initial and final, total momentum should remain same.
As the mass $3M$ is initially at rest, both the particles will move with momentum, having same magnitude & opposite direction, so that their total final momentum will also be zero.

As the magnitude of momentum of $M$ and $2M$ is the same, the de-Broglie wavelength of both the particles will be the same i.e. their ratio will be $1:1$.

Hence, $\left(D\right)$ is the correct answer.