Identify the correct statements in the following:(A) The total energy…

The correct answer is Option (1) → (C) and (D) only

In the Bohr model of hydrogen the electron moves in circular orbits with \( r_n \propto n^{2} \) and total energy \( E_n = -13.6/n^{2} \) eV.

(A) The total energy of an electron in n^th orbit in hydrogen atom is (−13.6/n) eV. — Incorrect. The energy varies as \( 1/n^{2} \), not \( 1/n \).

    \( \displaystyle E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \)

(B) As per Bohr’s theory, the stationary orbits of electrons around the nucleus are equally spaced. — Incorrect. The radii are \( r_1, 4r_1, 9r_1, \ldots \) since \( r_n \propto n^{2} \), so the gaps grow with n.

(C) Orbits of electrons around nucleus as per Bohr’s theory are circular. — Correct. Bohr assumed circular orbits, with the Coulomb force providing the centripetal force.

(D) The potential energy of electron in orbit in the hydrogen atom is twice of its total energy. — Correct. For an inverse-square force, \( K = -E \) and \( U = 2E \).

    \( \displaystyle K = \frac{ke^{2}}{2r},\quad U = -\frac{ke^{2}}{r},\quad E = K + U = -\frac{ke^{2}}{2r} \)

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

    \( \displaystyle E = K + U = \frac{e^2}{8\pi\varepsilon_0 r} - \frac{e^2}{4\pi\varepsilon_0 r} = -\frac{e^2}{8\pi\varepsilon_0 r} \qquad (12.4) \)”

Bohr Model of the Hydrogen Atom – “… Since 1 eV = 1.6 × 10^–19 J, Eq. (12.9) can be rewritten as

    \( \displaystyle E_n = -\frac{13.6\ \mathrm{eV}}{n^2} \qquad (12.10) \)”