Question:
Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6Å$. The radius of the third Bohr orbit of $He^+$is _______ picometer. (Nearest Integer)
Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6Å$. The radius of the third Bohr orbit of $He^+$is _______ picometer. (Nearest Integer)
Updated On: Mar 20, 2025
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Correct Answer: 270
Solution and Explanation
The radius of the \(n\)-th Bohr orbit is given by:
\[
r_n = r_1 \frac{n^2}{Z}
\]
For \(n = 3\) and \(Z = 2\):
\[
r_{\text{He}^{+}} = 0.6 \times \frac{3^2}{2} = 2.7 \, \text{Å}
\]
Converting to picometers:
\[
2.7 \, \text{Å} = 270 \, \text{pm}
\]
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