Atoms in the n=2 state can spontaneously emit photons having wich of the following energies ?

It's often helpful to draw a diagram showing the energy levels for the particular element you're interested in. The diagram for hydrogen is shown above.

The n = 1 state is known as the ground state, while higher n states are known as excited states. If the electron in the atom makes a transition from a particular state to a lower state, it is losing energy. To conserve energy, a photon with an energy equal to the energy difference between the states will be emitted by the atom.

Consider the photon emitted when an electron drops from the n=4 to the n=2 state to the photon emitted when an electron drops from n=3 to n=2. Which photon has the longer wavelength?

The photon emitted in the n=4 to n=2 transition
The photon emitted in the n=3 to n=2 transition
The smaller the energy the longer the wavelength. The photon has a smaller energy for the n=3 to n=2 transition.

In the hydrogen atom, with Z = 1, the energy of the emitted photon can be found using:

E = (13.6 eV) [1/nf2 - 1/ni2]

Atoms can also absorb photons. If a photon with an energy equal to the energy difference between two levels is incident on an atom, the photon can be absorbed, raising the electron up to the higher level.

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