Q7 CQ - College Physics (Urone)

Question

Explain how an α particle can have a larger range in air than a β particle with the same energy in lead.

Step-by-Step Solution

Answer

\({\rm{\alpha }}\) Particle with same energy can have more range in air than a \({\rm{\beta }}\) particle in lead.

Step 1: Significance of alpha and beta particle

While beta particles constitute a major health risk if consumed or breathed, alpha particles do not directly or externally cause radiation harm. Some beta particles have the potential to penetrate the skin and harm, including skin burns. When beta-emitters are eaten or inhaled, they pose the greatest risk.

Step 2: α particle can have a larger range in air than a β particle

The standard relation for a free particle shows that,

\(\begin{align}E &= \frac{1}{2}m{v^2}\\v &= \sqrt {\frac{{2E}}{m}} \\v \propto \frac{1}{{\sqrt m }}\end{align}\)

 

A radiation particle's speed will decrease as its mass increases.

Here, v is the speed of the particle, E is the total energy of the radiation particle and m is the mass of the radiation particle.

Because the mass of the \(\alpha \)-particle is over 1000 times more than that of the \(\beta \)-particle in this scenario, its speed will be substantially slower than that of a \(\beta \)-particle with the same amount of energy. Since the \(\alpha \)-particles will move more slowly and their time spent interacting with the medium particles will be longer, the speed of the medium will dampen more quickly. Since \(\beta \)-particles go farther and faster than lead medium particles, they can easily pass them.

Hence \({\rm{\alpha }}\) particle with same energy can have more range in air than a \({\rm{\beta }}\) particle in lead.