Question

A nucleus, initially at rest, decays radioactively. In the process, it emits an electron horizontally to the east, with momentum 9.0 X 10^–21 kg·m/s and a neutrino horizontally to the south, with momentum 4.8 X 10^–21 kg·m/s.

(a) In what direction does the residual nucleus move? (3 marks)

(b) What is the magnitude of its momentum? (3 marks)

(c) If the mass of the residual nucleus is 3.6 X 10^–25 kg, what is its recoil velocity? (3 marks)

Answer 1

(a) Determine the direction:

$$0=p_{Er}+p_{Ee}→p_{Er}=-p_{Ee},\\ 0=p_{Sr}+p_{Sn}→p_{Sr}=-p_{Sn},\\\space\\ \theta_r=\arctan\dfrac{p_{Sr}}{p_{Ee}}=\\\space\\=\arctan\dfrac{-4.8 · 10^{–21}}{-9.0 · 10^{–21}}=28°\text{N of W}$$

(b) Determine the magnitude:

$$p_r=\sqrt{p^2_{Er}+p^2_{Nr}}=\\\space\\ =\sqrt{(-4.8 · 10^{–21})^2+(-9 · 10^{–21})^2}=1.02·10^{-20}\text{ kg}·\text m/\text s.$$

(c) Determine the velocity:

$$v=p_r/m=28.3\text{ km/s}.$$