The ground state energy of hydrogen atom is −13.6 eV. The kinetic and potential energies of the electron in this state will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Kinetic energy of the electron = 13.6 eV; potential energy of the electron = −27.2 eV
In Bohr's model the Coulomb attraction provides the centripetal force on the electron:
\( \displaystyle \frac{mv^{2}}{r} = \frac{ke^{2}}{r^{2}} \;\Rightarrow\; K = \frac{1}{2}mv^{2} = \frac{ke^{2}}{2r} \)
\( \displaystyle U = -\frac{ke^{2}}{r} = -2K \qquad E = K + U = -\frac{ke^{2}}{2r} = -K \)
So the kinetic energy is \( -E \) and the potential energy is \( 2E \).
\( E = -13.6\,\mathrm{eV} \)
\( K = -E = 13.6\,\mathrm{eV} \)
\( U = 2E = -27.2\,\mathrm{eV} \)
Kinetic energy can never be negative, which rules out Options (2) and (4) at once, and Option (3) does not satisfy \( K + U = E \).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
