The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV. (a) What is the kinetic energy of the electron in this state? (b) What is the potential energy of the electron in this state? (c) Which of the answers above would change if the choice of the zero of potential energy is changed?

Ans (a).

Total energy of the electron, E = -3.4 eV

Kinetic energy of the electron is equal to the negative of the total energy.

=> K = -E              =>    – (- 3.4) = +3.4 eV

Hence, the kinetic energy of the electron in the given state is +3.4 eV.

Ans (b).

Potential energy (U) of the electron is equal to the negative of twice of its kinetic energy.

=» U = -2 K => – 2 x 3.4 = – 6.8 eV

Hence, the potential energy of the electron in the given state is – 6.8 eV.

Ans (c).
The potential energy of a system depends on the reference point taken. Here, the potential energy of the reference point is taken as zero. If the reference point is changed, then the value of the potential energy of the system also changes. Since total energy is the sum of kinetic and potential energies, total energy of the system will also change.