Calculate the radius of the fourth Bohr orbit (n = 4) of a Be³⁺ ion (nuclear charge Z = 4). Use the Bohr radius a₀ = 0.529 Å.
Answer
r₄ = 2.12 Å = 2.12×10⁻¹⁰ m
The correct answer is r₄ = 2.12 Å = 2.12×10⁻¹⁰ m — Round to three significant figures: r₄ ≈ 2.12 Å, and convert to metres (1 Å = 10⁻¹⁰ m).
Step-by-step solution
- Write the Bohr‑radius formula for a hydrogen‑like ion: r_n = .
- Substitute n = 4, Z = 4 and a₀ = 0.529 Å into the formula.
- Compute n²/Z = 4²/4 = 16/4 = 4.
- Multiply the result by a₀: r₄ = 4 × 0.529 Å = 2.116 Å.
- Round to three significant figures: r₄ ≈ 2.12 Å, and convert to metres (1 Å = 10⁻¹⁰ m).
Common mistake: Multiplying by Z instead of dividing by Z
Concept tested: Bohr radius for hydrogen‑like ions
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