The ratio of specific charges of α-particle and deuteron is — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Define Specific Charge The **specific charge** of any particle is the ratio of its electrical charge ($q$) to its mass ($m$): $$\text{Specific Charge} = \frac{q}{m}$$ --- ### Step 2 - Calculate the Specific Charge of an $\alpha$-Particle An $\alpha$-particle is a helium nucleus ($^{4}_{2}\text{He}^{2+}$) containing 2 protons and 2 neutrons: * Charge: $q_{\alpha} = 2e$ * Mass: $m_{\alpha} \approx 4\text{ amu}$ $$\left(\frac{q}{m}\right)_{\alpha} = \frac{2e}{4\text{ amu}} = 0.5\left(\frac{e}{\text{amu}}\right)$$ --- ### Step 3 - Calculate the Specific Charge of a Deuteron A deuteron is the nucleus of deuterium ($^{2}_{1}\text{H}^{+}$) containing 1 proton and 1 neutron: * Charge: $q_{d} = 1e$ * Mass: $m_{d} \approx 2\text{ amu}$ $$\left(\frac{q}{m}\right)_{d} = \frac{1e}{2\text{ amu}} = 0.5\left(\frac{e}{\text{amu}}\right)$$ --- ### Step 4 - Calculate the Ratio of Their Specific Charges $$\text{Ratio} = \frac{\left(\frac{q}{m}\right)_{\alpha}}{\left(\frac{q}{m}\right)_{d}} = \frac{0.5}{0.5} = \boxed{1:1}$$ --- ### Step 5 - Systematic Analysis of the Options * **Option (A) $1:2$:** Incorrect. This confuses the charge ratio (2:1 not 1:2) or the mass ratio. * **Option (B) $2:1$:** Incorrect. This is the ratio of their individual charges ($2e:1e$) or masses ($4:2$), not specific charges. * **Option (C) $1:1$:** Correct. Both particles have the same specific charge of $0.5$ in atomic units. * **Option (D) $4:1$:** Incorrect. This does not correspond to any correct calculation of their charge-to-mass ratios. $$\text{Correct Option: } \boxed{\text{C}}$$