A hydrogen atom is initially in its ground state and absorbs a photon of energy 10.2 eV. Assuming the photon is absorbed completely and the atom remains bound, find the principal quantum number N of the excited state reached by the electron.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A hydrogen atom is initially in its ground state and absorbs a photon of energy 10.2 eV. Assuming the photon is absorbed completely and the atom remains bound, find the principal quantum number N of the excited state reached by the electron.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

Ground-state energy: E₁ = −13.6 eV. After absorbing 10.2 eV: E(final) = −13.6+10.2 = −3.4 eV. For hydrogen, Eₙ = −13.6 ÷ n². Thus, −13.6 ÷ n² = −3.4. Therefore, n² = 13.6 ÷ 3.4 = 4. Hence, n = 2. Therefore N = 2.