A hydrogen atom in a state having a binding energy (the energy required to remove an electron) of makes a transition to a state with an excitation energy (the difference in energy between the state and the ground state) of 10.2 eV. We have to find (a) the energy of the emitted photon; and (b) show this transition on an energy-level diagram for the hydrogen, labelling with the appropriate quantum numbers.

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(a)

The energy of the state which corresponds to a binding energy of will be

.

As the states of the hydrogen atom, in the Bohr’ model, have energies given by the relation

,

the state with energy will correspond to the quantum number

.

It is given that the hydrogen atom makes a transition to the state with excitation energy of 10.2 eV. The energy of this state will therefore be

The quantum number corresponding to this state is

.

The energy of the photon which is emitted when hydrogen atom makes a transition from the state with energy to the state with energy will be

(b)