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Radius or area of Bohr orbits using r proportional to n squared over Z

This type of question, asked 6 times: 2 May 2023 S1, 3 May 2023 S2, 15 May 2023 S1, 15 Apr 2026 S2, 18 Apr 2026 S1, 18 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    13
    The radius of innermost orbit of hydrogen atom is 5.3×10−115.3 \times 10^{-11} m. The radius of fourth allowed orbit of hydrogen atom is

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  2. Question 2

    3 May 2023 S2

    19
    The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

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  3. Question 3

    15 May 2023 S1

    36
    The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

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  4. Question 4

    15 Apr 2026 S2

    147
    In the hydrogen atom, radii of the first four Bohr orbits are related as

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  5. Question 5

    18 Apr 2026 S1

    146
    The triply ionized beryllium (Be+++\mathrm{Be^{+++}}) has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given Z=4Z = 4 for beryllium)

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  6. Question 6

    18 Apr 2026 S2

    146
    If the difference between (n+1)th(n + 1)^{th} Bohr radius and nthn^{th} Bohr radius is given by (n−1)th(n - 1)^{th} Bohr radius, then the value of n is

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