Question

The specific charge of proton is $$9.6\times {10}^{7}Ck{g}^{-1}$$, then for an $$\alpha$$-particle it will be:
(a) $$38.4\times {10}^{7}Ck{g}^{-1}$$
(b) $$19.2\times {10}^{7}Ck{g}^{-1}$$
(c) $$2.4\times {10}^{7}Ck{g}^{-1}$$
(d) $$4.8\times {10}^{7}Ck{g}^{-1}$$

Answer 1

Hint: Proton and alpha particles are both positive species. But they differ in their mass and charge. Alpha particle has more charge and mass when compared to a proton.

Complete step by step solution:
> In the question, it is given that the proton has specific charge of $$9.6\times {10}^{7}Ck{g}^{-1}$$
> Let us consider Helium nucleus. It is also called an alpha particle and has a charge of +2 on it.
> We know that a specific charge of a proton is the charge on a proton divided by the mass of the proton in the particle. Alpha particle is actually a doubly ionised helium atom with +2 charge. This is twice the charge of the proton and it also has a mass which is almost four times than that of the mass of a proton since there are two protons and two neutrons in the nucleus of Helium.
> Specific charge of a proton can be written as =$${\displaystyle \frac{+e}{m_p}}$$, where $$+e$$ is the charge on the proton and $$m_p$$ is the mass of the proton.
> Now, for the alpha particle, $$+e$$ is double. That is the numerator becomes $$+2e$$. The mass of the alpha particle is 4 x mass of proton, so the denominator of the equation will be $$4m_p$$.
Also, Specific charge of alpha particle=$${\displaystyle \frac{+2e}{4m_p}}$$= $${\displaystyle \frac{+e}{m_p}}\times {\displaystyle \frac{1}{2}}$$=specific charge of proton $$\times {\displaystyle \frac{1}{2}}$$
Substituting the value of specific charge of proton in the above equation, we get
Specific charge of proton=$${\displaystyle \frac{9.6\times {10}^7}{2}}Ck{g}^{-1}=4.8\times {10}^{7}Ck{g}^{-1}$$.
Therefore, the correct option to the question is option (d) $$4.8\times {10}^{7}Ck{g}^{-1}$$

Note: The relation between the alpha particle and proton should be known to solve such problems. Specific charge is the ratio of a particle’s charge and its mass measured in Coulombs per kilogram and charge is measured in coulombs.