Match List I with List II for an electron in the $n^{\text{th}}$ orbit of a hydrogen atom.

List I (Physical Quantity) List II (Proportionality)
A. Orbital radius I. $n^3$
B. Kinetic energy II. $n$
C. Time period of revolution III. $n^{-2}$
D. Angular momentum IV. $n^2$

Choose the correct answer from the options given below:

Question

Match List I with List II for an electron in the

n^{\text{th}}

orbit of a hydrogen atom.

Choose the correct answer from the options given below:

Quantrex Academy · Accepted Answer

Correct answer: C. A - IV, B - III, C - I, D - II

According to Bohr's model of the hydrogen atom:

A. Orbital radius

r_n \propto n^2

B. Kinetic energy

K_n = \dfrac{13.6}{n^2} \text{ eV} \propto n^{-2}

C. Time period of revolution

T_n = \dfrac{2\pi r_n}{v_n}

. Since

r_n \propto n^2

and

v_n \propto n^{-1}

,

T_n \propto \dfrac{n^2}{n^{-1}} = n^3

D. Angular momentum

L_n = \dfrac{nh}{2\pi} \propto n

Therefore, the correct match is A - IV, B - III, C - I, D - II.

Answer: A - IV, B - III, C - I, D - II

Match List I with List II for an electron in the n^ th orbit of a...