Question

The total energy of an electron in the first excited state of hydrogen is about $- 3.4 \,eV$. Its kinetic energy in this state is

• A. -3.4eV
• B. -6.8eV
• C. 6.8eV
• D. 3.4eV

Answer 1

Answer: (D)

3.4eV

Answer 2

The kinetic energy is equal to the negative of total energy. Kinetic energy of electron $K=\frac{Z e^{2}}{8 \pi \varepsilon_{0} r}$ Potential energy of electron $U=-\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{r}$ $\therefore$ Total energy $E=K+U=\frac{Z e^{2}}{8 \pi \varepsilon_{0} r}-\frac{Z e^{2}}{4 \pi \varepsilon_{0} r}$ or $E=-\frac{Z e^{2}}{8 \pi \varepsilon_{0} r}$ or $E=-K$ or $K=-E=-(-3.4)=3.4 \,eV$