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Consider two different hydrogen atoms. The electron in each atom is in an excited state.

(a) Is it possible for the electrons to have different energies but the same orbital angular momentum L, according to the Bohr model? Justify.

No.Electrons within the same obital angular momentum L have the same energies according to Bohr model.

(b) Is it possible for the electrons to have different energies but the same orbital angular momentum L, according to quantum mechanics? Justify.

Yes. According to quantum mechanics it is possible to have different energies within the same orbital angular momentum L. Energy is determined by N and angular momentum is determined by L. Different value of N are compatible with the same value of L.

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  1. Both answers are correct. In quantum mechanics, each N value can have L values up to N-1. Hence N=1 can have only L = 0, but N=2 can have L=0 or n=1, etc. (There is no N=0). All principal quantum numers allow an L=0 suborbital (angular momentum) state.

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