Question

How much heavier is an alpha particle than an electron?

Answer 1

Hint: We are supposed to compare the masses of an alpha particle and an electron. For that you could recall the masses of alpha particles and electrons that we normally use in numerical problems. While recalling the mass of the alpha particle, also consider the binding energy. After that you could simply take their ratio to get the answer.

Complete answer:
In the question, we are asked to find how much heavier the alpha particle is when compared to an electron. So, we are supposed to compare the masses of an alpha particle and an electron.

In order for us to compare the masses of alpha particles and electrons, we would obviously require their respective masses. You may recall that the mass of the electron is $9.11\times {{10}^{-31}}kg$. Now for the case of an alpha particle, if you are thinking of adding the masses of two neutrons and two protons together to determine the mass of the alpha particle, it is quite impossible. It is true that each alpha particle contains two protons and two neutrons but the sum of their masses doesn’t take the binding energy into account, thus we will end up in the wrong value. So, while calculating we could use $6.645\times {{10}^{-27}}kg$ as the mass of the alpha particle.

Now we could take the ratio of masses of electron and alpha particle,
$\dfrac{{{M}_{\alpha }}}{{{M}_{e}}}=\dfrac{6.645\times {{10}^{-27}}}{9.11\times {{10}^{-31}}}$
$\Rightarrow \dfrac{{{M}_{\alpha }}}{{{M}_{e}}}=7294$
$\therefore {{M}_{\alpha }}=7294{{M}_{e}}$

Therefore, we found that the alpha particle is 7294 times more massive than an electron.

Note:
Incase if you are wondering what indeed the binding energy is, it is defined as the smallest amount of energy that would be required for removing a particle from a system or otherwise it is the energy required to disassemble them into individual parts. It is given by the following relation,
$\Delta B.E=\Delta M{{c}^{2}}$