Match List - I with List - II.
| List – I | List – II | ||
|---|---|---|---|
| (A) | Orbital radius of electron | (I) | \( \propto\displaystyle\frac{1}{n} \) |
| (B) | Orbital velocity of electron | (II) | \( \propto n \) |
| (C) | Orbital frequency of electron | (III) | \( \propto\displaystyle\frac{1}{n^{3}} \) |
| (D) | Angular momentum of electron | (IV) | \( \propto n^{2} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
In Bohr's model of hydrogen the nth orbit has radius \( r_n\propto n^{2} \) and speed \( v_n\propto 1/n \), and the angular momentum is quantised as \( L = nh/2\pi \).
(A) Orbital radius of electron — this matches (IV) \( \propto n^{2} \). \( r_n = n^{2}r_1 \).
(B) Orbital velocity of electron — this matches (I) \( \propto 1/n \). \( v_n = v_1/n \).
(C) Orbital frequency of electron — this matches (III) \( \propto 1/n^{3} \). The frequency is the speed divided by the circumference, so:
\( \displaystyle f = \frac{v}{2\pi r}\propto\frac{1/n}{n^{2}} = \frac{1}{n^{3}} \)
(D) Angular momentum of electron — this matches (II) \( \propto n \). \( L = nh/2\pi \).