Hydrogen atoms, initially at rest, undergo electron transitions. In the first case, the transition is from n=2 to n=1 . In the second case, the transition is from n=3 to n=1 . The ratio of the recoil kinetic energies of the hydrogen atoms i

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Hydrogen atoms, initially at rest, undergo electron transitions. In the first case, the transition is from n=2 to n=1 . In the second case, the transition is from n=3 to n=1 . The ratio of the recoil kinetic energies of the hydrogen atoms in the first case to the second case is

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Correct answer: D. 729 : 1024

The energy of a photon emitted during a transition is given by E = 13.6 ( 1 n_f^2 - 1 n_i^2 ) eV . For the first transition ( n=2 n=1 ): E₁ ( 1 1^2 - 1 2^2 ) = 1 - 1 4 = 3 4 For the second transition ( n=3 n=1 ): E₂ ( 1 1^2 - 1 3^2 ) = 1 - 1 9 = 8 9 The ratio of the emitted photon energies is: E₁ E₂ = 3/4 8/9 = 27 32 By conservation of momentum, the recoil momentum of the hydrogen atom equals the momentum of the emitted photon, p = E c . The recoil kinetic energy of the atom is given by K = p^2 2m = E^2 2mc^2 . The

Hydrogen atoms, initially at rest, undergo electron transitions. In the first case, the transition is from n=2 to n=1 . In the second case, the transition is from n=3 to n=1 . The ratio of the recoil kinetic energies of the hydrogen atoms in the first case to the second case is

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