According to Bohr's Model
(A) The radius of the orbiting electron is directly proportional to 'n'.
(B) The speed of the orbiting electron is directly proportional to '1/n'.
(C) The magnitude of the total energy of the orbiting electron is directly proportional to '\( 1/n^{2} \)'.
(D) The radius of the orbiting electron is directly proportional to '\( n^{2} \)'.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B), (C) and (D) only
In Bohr's model of a hydrogen-like atom the radius, speed and energy of the electron in the \( n \)th orbit are
\( \displaystyle r_n = \frac{n^{2} h^{2}\varepsilon_0}{\pi m Z e^{2}} \propto n^{2} \qquad v_n = \frac{Z e^{2}}{2\varepsilon_0 n h} \propto \frac{1}{n} \qquad E_n = -\frac{13.6\,Z^{2}}{n^{2}}\,\mathrm{eV} \propto \frac{1}{n^{2}} \)
(A) The radius of the orbiting electron is directly proportional to 'n'. — Incorrect. The radius grows as \( n^{2} \), not \( n \).
(B) The speed of the orbiting electron is directly proportional to '1/n'. — Correct. \( v_n \propto 1/n \), so the electron moves more slowly in outer orbits.
(C) The magnitude of the total energy of the orbiting electron is directly proportional to '\( 1/n^{2} \)'. — Correct. \( |E_n| = 13.6\,Z^{2}/n^{2}\,\mathrm{eV} \).
(D) The radius of the orbiting electron is directly proportional to '\( n^{2} \)'. — Correct. \( r_n = 0.529\,n^{2}/Z\,\mathring{\mathrm{A}} \).
Note: Statements (A), (C) and (D) of this question are from the latest textbook (2026-27). Statement (B), that the speed of the orbiting electron is proportional to 1/n, is printed only in the pre-rationalised textbook (2022-23). It was removed from the latest book, but the velocity of the electron in an orbit is still in the CUET 2026 syllabus, so do not skip it.
NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… The radius of nth possible orbit thus found is
\( \displaystyle r_n = \frac{n^2}{m}\left(\frac{h}{2\pi}\right)^2 \frac{4\pi\varepsilon_0}{e^2} \qquad (12.7) \)”
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
\( \displaystyle E_n = -\frac{13.6\ \mathrm{eV}}{n^2} \qquad (12.10) \)”
NCERT (Pre-rationalised edition, 2022-23):
Bohr Model of the Hydrogen Atom – “… Eq. (12.14) depicts that the orbital speed in the nth orbit falls by a factor of n.”