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Energy of a level or a transition in a hydrogen-like ion (E proportional to Z squared over n squared)

This type of question, asked 6 times: 2021 Paper 7, 31 Jan 2023, 1 Feb 2023, 11 Apr 2023, 2 Apr 2025, 7 Apr 2025. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 7

    18
    Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

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  2. Question 2

    31 Jan 2023

    117
    If the binding energy of ground state electron in a hydrogen atom is 13.6eV13.6eV, then, the energy required to remove the electron from the second excited state of Li2+Li^{2 +} will be: x×10−1eVx \times10^{- 1}eV. The value of xx is___
  3. Question 3

    1 Feb 2023

    94
    An electron of a hydrogen like atom, having Z=4Z = 4, jumps from 4th 4^{\text{th~}} energy state to 2nd 2^{\text{nd~}} energy state. The energy released in this process, will be: (Given Rch =13.6eV= 13.6eV ) Where R=R = Rydberg constant c=c = Speed of light in vacuum h=h = Planck's constant

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  4. Question 4

    11 Apr 2023

    104
    The energy of He+He^{+} ion in its first excited state is. (The ground state energy for the Hydrogen atom is −13.6eV)- 13.6eV) :

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  5. Question 5

    2 Apr 2025

    15
    Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of He+{He}^{+}ion in its first excited state. (B) the energy of H atom in ground state is same as that for Li++{Li}^{+ +}ion in its second excited state. (C) the energy of H atom in its ground state is same as that of He+{He}^{+}ion for its ground state. (D) the energy of He+{He}^{+}ion in its first excited state is same as that for Li++{Li}^{+ +}ion in its ground state Choose the correct answer from the options given below :

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  6. Question 6

    7 Apr 2025

    15
    In a hydrogen like ion, the energy difference between the 2nd 2^{\text{nd~}} excitation energy state and ground is 108.8 eV . The atomic number of the ion is

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