Question

The total energy of an electron in the first excited state of the hydrogen atom is $-3.4\text{eV}$. Find out its potential energy in this state.

Answer 1

Step 1. Formula for total energy

• The total energy is the sum of the kinetic and potential energies.

$\text{Total energy=Kinetic energy+Potential energy}$

Step 2: Calculation of kinetic energy:

The kinetic energy of the electron is equal to the negative of the total energy in its first excited state.

$\mathrm{Kinetic}\mathrm{energy}=-\mathrm{E}=-(-3.4)=+3.4\hspace{0.17em}\mathrm{eV}$

Step 3. Calculation of potential energy

$$\begin{gathered} \text{-3.4 eV= 3.4 eV+Potential energy} \\ \text{Potential energy=- 6.8 eV} \end{gathered}$$

Hence, the potential energy in this state is $-6.8\text{eV}$.