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A sample of He ^+ ions in the ground state is irradiated with monochromatic photons of energy 51.0 eV . The maximum number of spectral lines emitted when these ions subsequently de-excite to the ground state is

Correct answer

6

Step-by-step solution

The energy of an electron in a hydrogen-like species is given by E_n = -13.6 Z^2 n^2 eV . For the ground state of He ^+ ( Z = 2, n = 1 ), the energy is: E₁ = -13.6 2^2 1^2 = -54.4 eV When the ions absorb a photon of energy 51.0 eV , the energy of the excited state becomes: E_n = -54.4 + 51.0 = -3.4 eV Using the energy formula to find the principal quantum number n of the excited state: -3.4 = -13.6 2^2 n^2 -3.4 = - 54.4 n^2 n^2 = 54.4 3.4 = 16 n = 4 The maximum number of spectral lines emitted when the ions de-exci

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