Question

Deuterium is an isotope of hydrogen. Calculate the specific charge of deuteron (charge of electron $=1.6\times {10}^{-19}\mathrm{C}$; mass of proton $=1.67\times {10}^{-27}\mathrm{Kg}$; mass of neutron =$=1.72\times {10}^{-27}\mathrm{Kg}$.

• A. $2.3\times {10}^7\mathrm{C}/\mathrm{kg}$
• B. $1.15\times {10}^7\mathrm{C}/\mathrm{kg}$
• C. $0.575\times {10}^8\mathrm{C}/\mathrm{kg}$
• D. $3.45\times {10}^8\mathrm{C}/\mathrm{kg}$

Answer 1

The correct option is A

$2.3\times {10}^7\mathrm{C}/\mathrm{kg}$

The explanation of the correct option:

1. The specific charge is defined as the ratio of the charge of the particles to their mass.

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

2. Now, deuterium (D) is an isotope of hydrogen (H) atom having 1 proton, and 1 neutron in its nucleus.

3. Neutron has no charge, thus only the charge of the proton ($=1.6\times {10}^{-19}\mathrm{C}$) is considered.

4. Total mass = 2( mass of proton + mass of neutron)

5. Mass of proton = $1.67\times {10}^{-27}\mathrm{Kg}$ and mass of neutron =$=1.72\times {10}^{-27}\mathrm{Kg}$.

6. Therefore,

$$\begin{gathered} \mathrm{Specific}\mathrm{Charge}=\frac{1.6\times {10}^{-19}\mathrm{C}}{2({\mathrm{m}}_{\mathrm{p}}+{\mathrm{m}}_{\mathrm{n}})}=\frac{1.6\times {10}^{-19}\mathrm{C}}{2(1.67\times {10}^{-27}\mathrm{kg}+1.72\times {10}^{-27}\mathrm{kg})} \\ =\frac{1.6\times {10}^{-19}\mathrm{C}}{6.78\times {10}^{-27}\mathrm{kg}} \\ \therefore \mathrm{Specific}\mathrm{Charge}=2.3\times {10}^7\mathrm{C}/\mathrm{kg} \end{gathered}$$

Conclusion: The correct option is (a) $2.3\times {10}^7\mathrm{C}/\mathrm{Kg}$