Question

The penetrating powers of $\alpha$,$\beta$ and $\gamma$ radiations are in the order:

Answer 1

In this question, we will study the basics of a radioactive element and one by one learn each radiation on the basis of penetrating power. This will help us to get the required result. Further, we will know the basis of de Broglie wave- matter concept, for our better understanding.

Complete answer:
We know that radioactive material is defined as any material containing unstable atoms that emit ionizing radiation as it decays.
Here, we know that the ability of any radiation to damage molecules is defined as ionizing power. Also, when these particles interact with atoms, this interaction can cause the atom to lose its electrons and become ionized.
Penetration power is defined as the ability of radiation to pass through the matter is expressed. Here, we can also say that the more a radiation can pass through a material, the greater the penetration power and so, the more dangerous these radiations are.
Now, we see about the alpha particles: they have approximately four times the mass of a proton and neutron and approx 8,000 times the mass of a beta particle. Here, the alpha particles have the least penetrating power. These alpha particles can be stopped by a thick sheet of paper or even a layer of clothes.
Now, we see about the beta particles: these are much smaller than alpha particles and so, they have much less ionizing power or we can say less ability to damage tissue. Due to their small size they have much greater penetration power.
Now, we compare for Gamma particles: here gamma rays are energy that has no mass or charge. Gamma rays have tremendous penetration power
So, we can conclude that Gamma rays are the most penetrating of all the other radiations
Therefore, our order will be $\alpha < \beta < \gamma$.

Additional information:
Wave- particle duality is a concept of quantum mechanics that according to this every particle may be described as either a particle or a wave. It expresses the inability of the classical concepts of particle and wave, to fully describe the behavior of quantum scale objects.
In general, an electron in a metal has a de-Broglie wavelength in order of ~10nm. So, we observe quantum-mechanical effects in the properties of a metal when the width of the sample is around this value. The S.I unit of this wavelength is meter (m).
De-Broglie won the Nobel Prize for physics in 1929, after the wave- like behavior of matter was experimentally demonstrated in 1927.
As we know, time is defined by its measurement. Time is what a clock reads. In classical and non- relativistic physics, it is a scalar quantity. We know that length, mass and charge is usually described as a fundamental quantity, similarly time is also a fundamental quantity. The S.I unit of time is second.

Note:
We should remember that the penetrating power of a radioactive element also depends on its mass. Also, radioactivity does not depend on temperature and pressure. if a particle is larger than its de-Broglie wavelength, or if it is interacting with other objects on a scale significantly larger than its de Broglie wavelength, then its wave- like properties are not acceptable.