Question

A stationary nucleus undergoes alpha decay. In alpha decay, a helium nucleus is "kicked out" of the parent nucleus. The daughter particles are the alpha particle (the small, low mass, helium nucleus) and the remainder of the large, massive, nucleus.
How do the momentum magnitudes and the kinetic energy amounts for these particles compare immediately after the decay?

• A. Momentum Magnitudes - Kinetic Energy Amounts, same for both particles - greater for alpha particle
• B. Momentum Magnitudes - Kinetic Energy Amounts, same for both particles - same for both particles
• C. Momentum Magnitudes - Kinetic Energy Amounts, greater for alpha particles - greater for massive nucleus
• D. Momentum Magnitudes - Kinetic Energy Amounts, same for both particles - greater for massive nucleus
• E. Momentum Magnitudes - Kinetic Energy Amounts, greater for alpha particle - same for both particles

Answer 1

The correct option is A Momentum Magnitudes - Kinetic Energy Amounts, same for both particles - greater for alpha particle

Initial momentum of the system is zero. Thus according to the law of conservation of momentum, the final momentum of the system must also be zero. Hence the magnitude of momenta is same form both particles.

$\therefore$ $P_{\alpha }=P_{nucleus}=P=constant$

Kinetic energy of each particle, $K.E=\frac{P^2}{2m}$ $⟹$ $K.E\propto \frac{1}{m}$ ($\because P=constant$)

As the alpha particle has less mass compared to the remained nucleus, thus alpha particle will have greater kinetic energy.