If \( K \) and \( U \) represent kinetic and potential energies of an electron in an orbit of a hydrogen atom, then
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( K = -0.5U \)
In the Bohr model the Coulomb attraction of the nucleus provides the centripetal force on the electron.
\( \displaystyle \frac{mv^{2}}{r} = \frac{ke^{2}}{r^{2}} \Rightarrow K = \frac{1}{2}mv^{2} = \frac{ke^{2}}{2r} \)
\( \displaystyle U = -\frac{ke^{2}}{r} \)
\( K = -U/2 = -0.5\,U \)
The total energy is \( E = K + U = -K \), negative for a bound electron.
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.)”