Chemistry - Atomic Structure Question with Solution | TestHub

The Bohr model provides formulas for various properties of a single-electron species.

Radius of orbit: $r_{n,z}\propto \frac{n^2}{Z}$

Speed of electron: $V_{n,z}\propto \frac{Z}{n}$

Time period of revolution: $T_{n,z}\propto \frac{n^3}{Z^2}$

Kinetic energy: $K_{n,z}\propto \frac{Z^2}{n^2}$

Let's calculate the ratios:

(A) $r_{2,1}:r_{1,2}=\frac{2^2}{1}:\frac{1^2}{2}=4:\frac{1}{2}=8:1$ (Matches Q)

(B) $V_{1,3}:V_{3,1}=\frac{3}{1}:\frac{1}{3}=3:\frac{1}{3}=9:1$ (Matches P)

(C) $T_{1,2}:T_{2,1}=\frac{1^3}{2^2}:\frac{2^3}{1^2}=\frac{1}{4}:8=1:32$ (Matches S)

(D) $K_{1,2}:K_{2,1}=\frac{2^2}{1^2}:\frac{1^2}{2^2}=4:\frac{1}{4}=16:1$ (Matches R)

Therefore, the correct matching is A-Q, B-P, C-S, D-R. This corresponds to option (B).