e/m ratio of a particle of charge 2 unit and mass 4 amu is — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Definition of Specific Charge $$\text{Specific Charge} = \frac{q}{m}$$ ### Step 2 - Convert Charge to SI Units Given charge = 2 units: $$q = 2 \times 1.6 \times 10^{-19}\text{ C} = 3.2 \times 10^{-19}\text{ C}$$ ### Step 3 - Convert Mass to SI Units Given mass = 4 amu: $$m = 4 \times 1.66 \times 10^{-27}\text{ kg} = 6.64 \times 10^{-27}\text{ kg}$$ ### Step 4 - Calculate e/m $$\frac{e}{m} = \frac{3.2 \times 10^{-19}}{6.64 \times 10^{-27}} = \frac{3.2}{6.64} \times 10^{8} \approx 0.482 \times 10^8 = \boxed{4.8 \times 10^7 \text{ C/kg}}$$ ### Step 5 - Evaluation of Options * **Option (A) $4.8 \times 10^7$ C/kg:** Correct — matches our calculation. * **Option (B) 0.5 C/kg:** Incorrect — dividing 2/4 without unit conversion. * **Option (C) $4.8 \times 10^4$ C/kg:** Incorrect — wrong power of ten. * **Option (D) $8 \times 10^{-20}$ C/kg:** Incorrect — no physical basis. $$\text{Correct Option: } \boxed{\text{A}}$$