The kinetic energy of an electron in ground level in hydrogen atom is K units. The values of its potential energy and total energy respectively are ____________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( -2K;\ -K \)
In the Bohr model the electron moves in a circle under the Coulomb attraction of the nucleus:
\( \displaystyle \frac{m v^{2}}{r} = \frac{k e^{2}}{r^{2}} \;\Rightarrow\; K = \frac{1}{2} m v^{2} = \frac{k e^{2}}{2r} \)
The potential energy of the electron-proton pair is
\( \displaystyle U = -\frac{k e^{2}}{r} = -2K \)
The total energy is
\( \displaystyle E = K + U = K - 2K = -K \)
Note: The same question was also asked in CUET (UG) 2026 on 20-05-2026 (Slot 1).
NCERT (2026-27):
Electron Orbits – “… The kinetic energy (K) and electrostatic potential energy (U) of the electron in hydrogen atom are
\( \displaystyle K = \frac{1}{2}mv^2 = \frac{e^2}{8\pi\varepsilon_0 r} \quad \text{and} \quad U = -\frac{e^2}{4\pi\varepsilon_0 r} \)
(The negative sign in U signifies that the electrostatic force is in the –r direction.) Thus the total energy E of the electron in a hydrogen atom is
\( \displaystyle E = K + U = \frac{e^2}{8\pi\varepsilon_0 r} - \frac{e^2}{4\pi\varepsilon_0 r} = -\frac{e^2}{8\pi\varepsilon_0 r} \qquad (12.4) \)”