Question

The ratio of specific charge of a proton and an $\alpha$- particle is:
(a)2:1
(b)1:1
(c)1:4
(d)1:2

Answer 1

Hint : Proton is a subatomic particle with a positive charge of +1e elementary charge and has mass slightly less than a neutron. $\alpha$ particles consist of two protons and 2 neutrons which are bound together into a particle which is identical to the Helium nucleus. Specific charge of a particle is ratio of charge of the particle to its mass

Complete step by step solution :
The charge on a $\alpha$ particle is twice the charge of the proton while its mass is four times greater than proton.
We know that charge on a proton is = +e
Let us consider, Mass of a proton = m
And the charge on alpha particle or He = +2e
So we know that Mass of He = 4m
Specific charge is defined as the ratio of charge to mass and can be written as ($\dfrac{e}{m}$) = $\dfrac{e}{m}$-(i)
Specific charge for an alpha particle =$\dfrac{2e}{4m}$ __(ii) here, charge =2e and mass is 4m.
Therefore, the ratio of these two $\dfrac{e}{m}$ values (that is (i) and (ii) its ratios) is given as:
$\dfrac{e}{m}\times \dfrac{4m}{2e}=\dfrac{2}{1}$= 2:1.
Therefore, the charge to mass ratio of $\alpha$ particles is twice the charge to mass ratio of a proton.

The correct answer to the question is option (a).

Additional Information :
Usually mass to charge ratio is used. It is a physical quantity widely used in electrodynamics of charged particles, for example in ion optics. It has main uses in mass spectrometry, where we determine a molecule using the mass to charge ratio of its fragments produced, when an electron beam is bombarded on the molecule.

Note : Specific charge of a particle is the ratio of charge of the particle to its mass. Charge on an alpha particle is twice that of a proton and the mass is four times than that of a proton. For any other element as well do not forget to take the total charge (using Atomic number) and total mass (using mass number)