Answer to Question #85772 in Mechanics | Relativity for Ra

Question

In a nuclear reactor one dueterium atom (D) and one triton atom (T) at rest decay into on alpha particle (He) and one neutron (n). How to obtain an expression for the momentum of the alpha particle and the neutron?

Answer 1

After the decay process the alpha-particle and the neutron move with their own kinetic energies $T$:

$$T=\frac{1}{2}mv^2=\frac{1}{2}mv^2\cdot \frac{m}{m}=\frac{1}{2}m^2v^2\cdot \frac{1}{m}=\frac{1}{2m}p^2,$$

therefore

$$p=\sqrt{2Tm},$$

where $p$, $T$, and $m$ belong to the alpha particle or neutron correspondingly. But according to law of conservation of momentum since they will move in opposite direction, and this fact adds one more condition to our reasoning:

$$p_{\alpha}=-p_\text{n}.$$