For an atom, the attractive potential energy is V(r) = V₀ ln(r/r₀), where V₀ and r₀ are constants. Using Bohr quantization, determine how the radius r of the nth orbit depends on n.
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For an atom, the attractive potential energy is V(r) = V₀ ln(r/r₀), where V₀ and r₀ are constants. Using Bohr quantization, determine how the radius r of the nth orbit depends on n.

G1 Physics · Accepted Answer

Step 1: For V(r)=V₀ln(r/r₀), the force magnitude is V₀/r. Step 2: Circular motion gives mv²/r = V₀/r, so mv²=V₀ is constant. Step 3: Bohr quantization mvr=nh/(2π) then gives r ∝ n. Correct answer: A.