Comprehension IX A hydrogen-like atom of atomic number \( Z \) is in an excited state of quantum...

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Comprehension IX
A hydrogen-like atom of atomic number \( Z \) is in an excited state of quantum number \( 2 n \). It can emit a maximum energy photon of \( 204 \mathrm{eV} \). If it makes a transition to quantum state \( n \), a photon of energy \( 40.8 \mathrm{eV} \) is emitted.
What is the energy of ground state of this atom?
(a) \( -13.6 \mathrm{eV} \)
(b) \( -54.4 \mathrm{eV} \)
(c) \( -217.6 \mathrm{eV} \)
(d) \( -870.4 \mathrm{eV} \)
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