Question

Compared to $\mathit{\alpha }$particles with the same energy,$\mathit{\beta }$ particles can much more easily penetrate through matter. Why is this?

Short answer

As the speed of $\beta -$particle has the same energy, the speed of particle will be higher due to which the wavelength of a particle is decreased and helps the electron penetrate the matter. Therefore, compared to $\alpha -$particles with the same energy,$\beta -$particle can much more easily penetrate through matter

Step-by-step solution

Define the energy.

The energy $E$of a photon is inversely proportional to the wavelength $\lambda$of photon and directly proportional to the frequency $f$of wave.

$$\begin{gathered} E=hf \\ E=\frac{hc}{\lambda } \end{gathered}$$

Where, the value of Planck’s constant $h=6.626\times {10}^{-34}J·s$.

Explain the reason of when compared to α particles with the same energy, β particles can much more easily penetrate through matter.

Since the $\alpha -$particles have a larger mass so, the particles have higher energy while, the $\beta -$particle has the same energy due to which it has a higher speed. And also, due to this electron neglects the attractive force of charge nuclei of the matter.

Since the speed of $\beta -$particle is high then the wavelength of the particles decreases by the de Broglie wavelength equation $\lambda =\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$m\nu $}\right.$. Hence, the electron penetrates the matter.