Match List I with List II using Bohr's atomic model:
| LIST I | LIST II | ||
|---|---|---|---|
| A. | Radius of electron orbit | I. | directly proportional to 'n\( ^2 \)' |
| B. | Angular momentum of electron | II. | directly proportional to 'n' |
| C. | Velocity of electron | III. | inversely proportional to 'n' |
| D. | Energy of electron | IV. | inversely proportional to 'n\( ^2 \)' |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-I, B-II, C-III, D-IV
In Bohr's model the electron moves in a circular orbit whose angular momentum is quantised, \( L = n\hbar = nh/2\pi \). Combining this with the force balance gives the dependence of each quantity on the orbit number n.
(A) Radius of electron orbit — this matches (I) directly proportional to 'n\( ^2 \)'. The radius is \( r_n = n^{2}a_0 \), where \( a_0 \) is the Bohr radius.
(B) Angular momentum of electron — this matches (II) directly proportional to 'n'. Bohr's quantisation condition is \( L = nh/2\pi \).
(C) Velocity of electron — this matches (III) inversely proportional to 'n'. The speed is \( v_n = \displaystyle\frac{e^{2}}{2\varepsilon_0 h}\cdot\frac{1}{n} \).
(D) Energy of electron — this matches (IV) inversely proportional to 'n\( ^2 \)'. The energy is \( E_n = -\displaystyle\frac{13.6}{n^{2}}\,\mathrm{eV} \), whose magnitude varies as \( 1/n^{2} \).
Note: Items (A), (B) and (D) of this question are from the latest textbook (2026-27). Item (C), that the velocity of the electron is inversely proportional to 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 – “… Thus the angular momentum (L) of the orbiting electron is quantised. That is
\( \displaystyle L = nh/2\pi \qquad (12.5) \)”
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.”