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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0 will be: [hc = 12500 eV Å]

1. 4a0
2. 9a0
3. 25a0
4. 16a0

Correct answer: 16a0

Solution

Photon energy = 12500/980 = 12.76 eV. From n=1 (-13.6 eV) the atom reaches E = -13.6 + 12.76 = -0.85 eV = -13.6/n^2, giving n^2 = 16, n = 4. Radius = n^2 * a0 = 16 a0.

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