## Question

A hydrogen atom rises from its *n* = 1 state to the *n* = 4 state by absorbing energy. If the potential energy of the atom in *n* = 1 state be –13.6 eV, thencalculate : potential energy in *n* = 4 state.

### Solution

–0.85 *eV*

The energy of the *n*th level of hydrogen atom is given by

Where *R* is Rydberg’s constant, *h* is Planck’s constant and *c* is speed of light. Thus, the energy of the lowest level (*n* = 1) is given by

.

The energy of the fourth-level (*n* = 4) is

.

Here *E*_{1} = –13.6 eV. So, energy in the state *n* = 4 is

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