Question

The charge to mass ratio of $\alpha$- particle is approximately is_____ of the charge to mass ratio of a proton is:
A. Half
B. Twice
C. Four times
D. Six times

Answer 1

Hint: An alpha particle is actually a helium nucleus which consists of two protons and two neutrons so its charge is twice the proton’s charge and the mass is four times greater.

Complete answer:
Formula used: $\text{Specific charge = }{\displaystyle \frac{\text{charge}}{\text{mass of substance}}}$
Let the charge of the proton $=+\text{e}$
and the mass of the proton $=\text{m}$
As we know that alpha particle is a helium nucleus containing two protons and two neutrons
Therefore the charge of the alpha particle $=+2\text{e}$
and the mass of alpha particle $=4\text{m}$
Since, $\text{Specific charge = }{\displaystyle \frac{\text{charge}}{\text{mass of substance}}}$
Therefore for proton, specific charge $={\displaystyle \frac{\text{e}}{\text{m}}}$
And for alpha particle, specific charge $={\displaystyle \frac{\text{2e}}{4\text{m}}}$
Therefore the charge to mass ratio is:
$$\begin{gathered} ={\displaystyle \frac{{\displaystyle \frac{\text{e}}{\text{m}}}}{{\displaystyle \frac{2\text{e}}{4\text{m}}}}} \\ ={\displaystyle \frac{\text{e}}{\text{m}}}\times {\displaystyle \frac{4\text{m}}{2\text{e}}} \\ ={\displaystyle \frac{2}{1}} \end{gathered}$$
Hence the charge to mass ratio of an alpha particle is twice the charge to mass ratio of a proton.

Therefore the correct option is B.

Note: In this question we assumed the charge of the proton as $+\text{e}$ and the mass of the proton as $\text{m}$ therefore the charge of the alpha particle is $+2\text{e}$ and the mass of the alpha particle is $4\text{m}$, then we found the specific charge for both of them using the formula and after that we calculated that the charge to mass ratio of an alpha particle is twice the charge to mass ratio of a proton.