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.

 

[baba89]

I would like to provide a more detailed explanation for the question at hand. The penetrating power of a beta particle is determined by its ability to interact with matter and transfer its energy. This ability is influenced by several factors, including the mass and charge of the particle.

In the case of beta particles, they have a smaller mass compared to alpha particles. This means that they have a higher velocity and kinetic energy for the same amount of energy. When a beta particle collides with matter, it transfers some of its kinetic energy to the particles in the material. The amount of energy transferred depends on the mass of the particle it collides with. Since beta particles have a smaller mass, they transfer less energy per collision compared to alpha particles.

This leads to the concept of fractional loss of kinetic energy per collision. This refers to the percentage of energy that is transferred from the beta particle to the material it collides with. Since beta particles have a smaller mass, they experience a smaller fractional loss of kinetic energy per collision compared to alpha particles. This means that they can travel further through the material before their energy is completely absorbed.

To understand this concept mathematically, we can use the equation for kinetic energy (KE= 1/2 mv^2). Since beta particles have a smaller mass, they have a higher velocity for the same amount of energy. This results in a smaller value for the kinetic energy. When they collide with a material of a larger mass, the change in kinetic energy will be relatively small compared to the original value. This leads to a smaller fractional loss of kinetic energy per collision.

In summary, the mass of a particle plays a crucial role in determining its penetrating power. In the case of beta particles, their smaller mass allows them to transfer less energy per collision, making them more penetrating compared to alpha particles with the same kinetic energy. This can be explained mathematically by considering the equation for kinetic energy and the concept of fractional loss of energy per collision.