Question:
The Bohr orbit radius for the hydrogen atom (\( n = 1 \)) is approximately 0.530 Ã
. The radius for the first excited state (\( n = 2 \)) orbit is (in Ã
)
The Bohr orbit radius for the hydrogen atom (\( n = 1 \)) is approximately 0.530 Ã
. The radius for the first excited state (\( n = 2 \)) orbit is (in Ã
)
Show Hint
The radius of the Bohr orbit increases with the square of the principal quantum number \( n \).
Updated On: Mar 24, 2026
- 0.13
- 1.06
- 4.77
- 2.12
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Use the formula for the Bohr radius.
The radius for the \( n \)-th orbit is given by \( r_n = n^2 \times 0.53 \, \text{Ã } \).
Step 2: Calculate the radius for the first excited state.
For \( n = 2 \), the radius is \( r_2 = 2^2 \times 0.53 = 2.12 \, \text{Ã } \). Final Answer: \[ \boxed{2.12 \, \text{Ã }} \]
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