What is the total energy of electron in the nth stationary orbit of hydrogen atom?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{-13.6}{n^2}\,\mathrm{eV} \)
In the Bohr model the total energy of the electron is the sum of its kinetic energy and the (negative) electrostatic potential energy. It is negative because the electron is bound to the nucleus.
\( \displaystyle E_n = -\frac{me^{4}}{8\varepsilon_0^{2}h^{2}}\,\frac{1}{n^{2}} = -\frac{13.6}{n^{2}}\,\mathrm{eV} \)
NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… Atomic energies are often expressed in electron volts (eV) rather than joules. Since 1 eV = 1.6 × 10–19 J, Eq. (12.9) can be rewritten as
\( \displaystyle E_n = -\frac{13.6\ \mathrm{eV}}{n^2} \qquad (12.10) \)
The negative sign of the total energy of an electron moving in an orbit means that the electron is bound with the nucleus.”