Chemistry · Bohr model of a hydrogen atom: its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model
Some hydrogen-like atom in ground state absorb photons having the same energy an
Some hydrogen-like atom in ground state absorb \( n \) photons having the same energy and on de-excitation, it emits exactly \( n \) photons. Then the energy of absorbed photon may be: This question has multiple correct options
- A. \( 91.8 e V \)
- B. \( 40.8 e V \)
- C. \( 48.4 e V \)
- D. \( 54.4 e V \)
Step-by-step solution
For a hydrogen-like atom, the ground state energy is E₁ = -13.6Z² eV. Absorbing n photons of the same energy E_photon excites the atom to a level with principal quantum number m, so nE_photon = 13.6Z²(1 - 1/m²). Upon de-excitation, it emits exactly n photons, which is possible if n ≤ m-1. For n=1, m=2, and Z=2, we get E_photon = 40.8 eV. This matches option B.
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