An atom in an excited state has a lifetime of 12 ns; in a second excited state the lifetime is 23 ns. We have to find the uncertainty in energy for a photon emitted when an atom makes a transition between the two states.

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The lifetime of the first excited state is 12 ns. Therefore, uncertainty in the energy of this level will be

The lifetime of the second excited state is 23 ns. Therefore, uncertainty in the energy of this level will be

Therefore, the uncertainty in energy for a photon emitted when an atom makes a transition between the two states will be