Question

Hypothetical values of charge of electron, masses of proton and neutron are $3.2\times {10}^{-19}\mathrm{C}$, $8.35\times {10}^{-28}\mathrm{g}$ and $8.6\times {10}^{-28}\mathrm{g}$, respectively. Calculate the specific charge of an $\alpha$-particle.

• A. $5.6\times {10}^9\mathrm{C}/g$
• B. $3.8\times {10}^8\mathrm{C}/g$
• C. $1.9\times {10}^8\mathrm{C}/g$
• D. $0.95\times {10}^9\mathrm{C}/g$

Answer 1

The correct option is C

$1.9\times {10}^8\mathrm{C}/g$

Specific charge- It is the ratio of charge to mass.

$\mathrm{Specific}\mathrm{Charge}=\frac{\mathrm{Charge}}{\mathrm{Mass}}$

The explanation for the correct option:

1. An alpha particle is ${\mathrm{He}}^{2+}$ ion with 2 protons and 2 neutrons. It does not have any electrons.
2. Thus, an alpha particle has only the charge of 2 protons as neutrons do not carry any charge.
3. A magnitude of positive charge is the same as the magnitude of negative charge. Hence, the charge of proton= e = $3.2\times {10}^{-19}\mathrm{C}$.
4. Now, the total charge carried by an alpha particle (2 protons) = 2e
5. Next, the mass of alpha particle = (2$\times$mass of protons) + (2$\times$mass of neutrons) = 2m_p + 2m_n
6. Therefore, the specific charge of the $\alpha$particle is calculated as-

$$\begin{gathered} \mathrm{Specific}\mathrm{Charge}=\frac{2\mathrm{e}}{2{\mathrm{m}}_{\mathrm{p}}+2{\mathrm{m}}_{\mathrm{n}}}=\frac{2\mathrm{e}}{2({\mathrm{m}}_{\mathrm{p}}+{\mathrm{m}}_{\mathrm{n}})} \\ =\frac{\mathrm{e}}{({\mathrm{m}}_{\mathrm{p}}+{\mathrm{m}}_{\mathrm{n}})}=\frac{3.2\times {10}^{-19}\mathrm{C}}{(8.35\times {10}^{-28}\mathrm{g}+8.6\times {10}^{-28}\mathrm{g})} \\ \therefore \mathrm{Specific}\mathrm{Charge}=\frac{3.2\times {10}^{-19}\mathrm{C}}{16.95\times {10}^{-28}\mathrm{g}}=1.9\times {10}^8\mathrm{C}/\mathrm{g} \end{gathered}$$

7. Hence, the specific charge of the alpha particle is 1.9$\times$10⁸ C/g

The correct option is c).