Question

The Bohr orbit radius for the hydrogen atom (\( n = 1 \)) is approximately 0.530 Å. The radius for the first excited state (\( n = 2 \)) orbit is (in Å)

• A. 0.13
• B. 1.06
• C. 4.77
• D. 2.12

Hint:

The radius of the Bohr orbit increases with the square of the principal quantum number \( n \).

Answer 1

The Correct Option is D

Step 1: Use the formula for the Bohr radius.
The radius for the \( n \)-th orbit is given by \( r_n = n^2 \times 0.53 \, \text{Å} \).
Step 2: Calculate the radius for the first excited state.
For \( n = 2 \), the radius is \( r_2 = 2^2 \times 0.53 = 2.12 \, \text{Å} \). Final Answer: \[ \boxed{2.12 \, \text{Å}} \]