Penetrating power of a beta particle

[eftalia]

Hello! I've been quite puzzled by this question and its solution.

Explain why beta-particles penetrate through matter more easily compared with alpha-particles having the same KE?

The answer given goes: The mass of beta-particles are much smaller than those of alpha-particles, hence the fractional loss of kinetic energy per collision for beta-particles are smaller and therefore beta-particles are more penetrating.

Why is the fractional loss of KE per collision positively dependent on the masses? Is there a mathematical way to reason this out?

Thanks :)

 

[tiny-tim]

Welcome to PF!

Why is the fractional loss of KE per collision positively dependent on the masses? Is there a mathematical way to reason this out?

Hello eftalia! Welcome to PF!

Hint: write out the equations for conservation of momentum, and conservation of energy, of a mass m at speed v hitting a stationary mass M head-on, and see how the final speed depends on m.