Question

suppose that a particle at rest with mass m decays into a photon and another particle with mass m/2 , which recoilds in a direction opposite to the photon. Using the conservation of energy and momentum find the momentum of the recoiling particle

Answer 1

Answer:

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

Explanation:

To find the momentum of the recoiling particle you can use the momentum formula for a photon:

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

before the decay the momentum is zero. Hence, after the decay the momentum of the photon plus the momentum of the recoiling particle must be zero:

$p_a=p_b\\\\\frac{h}{\lambda}-\frac{m}{2}v=0\\\\p_r=\frac{m}{2}v=\frac{h}{\lambda}$

where pr is the momentum of the recoiling particle.