A hypothetical Bohr atom has potential energy U(r) = a ln(r ÷ r₀), where a > 0. For a circular orbit, the attractive force magnitude is a ÷ r. If Bohr quantization is imposed, which orbital quantity is independent of the principal quantum number n?
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Question

A hypothetical Bohr atom has potential energy U(r) = a ln(r ÷ r₀), where a > 0. For a circular orbit, the attractive force magnitude is a ÷ r. If Bohr quantization is imposed, which orbital quantity is independent of the principal quantum number n?

Options

G1 Physics · Accepted Answer

For a circular orbit, mv² ÷ r = a ÷ r. Multiplying by r: mv² = a. Thus, v = √(a ÷ m), which is independent of r and independent of n. Bohr quantization still gives mvr = nħ, so because v is constant, r is proportional to n. Correct option: B.