Answer:
[tex]p_r=\frac{h}{\lambda}[/tex]
Explanation:
To find the momentum of the recoiling particle you can use the momentum formula for a photon:
[tex]p=\frac{h}{\lambda}[/tex]
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:
[tex]p_a=p_b\\\\\frac{h}{\lambda}-\frac{m}{2}v=0\\\\p_r=\frac{m}{2}v=\frac{h}{\lambda}[/tex]
where pr is the momentum of the recoiling particle.
