Question

In the hydrogen atom, radii of the first four Bohr orbits are related as

• A. \(1:2:3:4\)
• B. \(\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\)
• C. \(1:4:9:16\)
• D. \(\frac{1}{4}:\frac{1}{9}:\frac{1}{16}\)

Hint:

Bohr radius r is proportional to n squared.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For hydrogen, \(r_n = r_1 n^2\), where \(r_1 = 0.529\) angstrom.

Step 2: Ratio
\[ r_1 : r_2 : r_3 : r_4 = 1^2 : 2^2 : 3^2 : 4^2 = 1 : 4 : 9 : 16 \]
Option (A) is the ratio of n itself, and (B) and (D) are inverse ratios.

Final Answer:
The radii are in the ratio 1 : 4 : 9 : 16, option (C). \[ \boxed{1:4:9:16} \]