A particle of mass at rest decays into two masses and with non-zero velocities. What is the ratio of of de Broglie wavelengths of particles?
Step 1. Formula used:
Here, is Planck’s constant.
is the speed of light.
is the de Broglie wavelength.
Step 2: Formula Used
Linear momentum of the particle mass moving with velocity ,
is the linear momentum of the particle.
Step 3. Calculating the ratio of de Broglie wavelength:
We know that, according to de Broglie's hypothesis, the momentum of the particle is,
Here, is Planck’s constant, is the speed of light,
is the de Broglie wavelength.
According to the law of conservation of momentum,
We can write,
is the velocity of the parent particle,
is the velocity
is the velocity of .
Since the parent particle with mass remains at rest, the initial velocity is zero.
Therefore, the above equation becomes,
The particle of mass and particle of mass has equal momentum.
So, we can write,
Since,
The wavelength of these particles is equal,
Therefore, the ratio of de Broglie wavelength of particles is .