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For a hydrogen-like species whose ground-state Bohr radius is a0, what is the de Broglie wavelength of the electron in the 3rd orbit?

1. a0/3
2. 9*a0
3. 2*pi*a0
4. 6*pi*a0

Correct answer: 6*pi*a0

Solution

Bohr's quantization condition: 2*pi*rₙ = n*lambda (circumference = n * de Broglie wavelength). For n=3: r₃ = 3² * a0 = 9*a0. Therefore lambda = 2*pi*9*a0/3 = 6*pi*a0.

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