Question:
The radius of the first Bohr orbit of hydrogen atom is 0.529 $\AA$. The radius of the third orbit $H^+$ will be ________.
The radius of the first Bohr orbit of hydrogen atom is 0.529 $\AA$. The radius of the third orbit $H^+$ will be ________.
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The radius of the first Bohr orbit of hydrogen atom is 0.529 $\AA$. The radius of the third orbit $H
Updated On: Apr 15, 2026
- 8.46 \AA
- 0.705 \AA
- 1.59 \AA
- 4.79 \AA
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The Correct Option is D
Solution and Explanation
Step 1: Formula
The radius of the $n^{th}$ orbit is $r_n = \frac{0.529 \times n^2}{Z} \text{\AA}$.
Step 2: Values
For Hydrogen, $Z = 1$. For the third orbit, $n = 3$.
Step 3: Calculation
$r_3 = \frac{0.529 \times (3)^2}{1} = 0.529 \times 9 = 4.761 \text{\AA}$.
Step 4: Conclusion
The closest value is 4.79 \AA.
Final Answer: (D)
The radius of the $n^{th}$ orbit is $r_n = \frac{0.529 \times n^2}{Z} \text{\AA}$.
Step 2: Values
For Hydrogen, $Z = 1$. For the third orbit, $n = 3$.
Step 3: Calculation
$r_3 = \frac{0.529 \times (3)^2}{1} = 0.529 \times 9 = 4.761 \text{\AA}$.
Step 4: Conclusion
The closest value is 4.79 \AA.
Final Answer: (D)
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