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1998

JEE Main 1998 Chemistry question on Atomic Structure

The energy of an electron in the first Bohr orbit of H-atom is −13.6-13.6 eV. The possible energy value(s) of the excited state(s) for electrons in Bohr orbits of hydrogen is (are)
  1. A.
    −3.4-3.4 eV
  2. B.
    −4.2-4.2 eV
  3. C.
    −6.8-6.8 eV
  4. D.
    +6.8+6.8 eV
Show answer and solution

Correct option: A

Solution

The energy of the nth Bohr orbit is En = -13.6/n² eV. For excited states, n = 2, 3, 4, ... giving allowed energies -3.4 eV (n=2), -1.51 eV (n=3), etc. Only -3.4 eV matches this formula (n=2). The values -4.2 eV and -6.8 eV do not correspond to any integer n, and +6.8 eV is positive which is impossible for a bound electron in hydrogen.

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