A hydrogen atom initially in its ground state absorbs a photon of energy 12.75 eV. The photon is exactly resonant with a bound-state excitation. If the electron reaches the Nth Bohr orbit, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A hydrogen atom initially in its ground state absorbs a photon of energy 12.75 eV. The photon is exactly resonant with a bound-state excitation. If the electron reaches the Nth Bohr orbit, find N.

G1 Physics · Accepted Answer

Initial energy: E₁ = −13.6 eV. Final energy after absorption: E(final) = −13.6+12.75 = −0.85 eV. For hydrogen, Eₙ = −13.6 ÷ n². Hence, 13.6 ÷ n² = 0.85. Therefore, n² = 13.6 ÷ 0.85 = 16. So, n = 4. Hence N = 4.