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Characteristics of Bohr's Atomic Model

The radius of...

Question

The radius of the Bohr orbit in the ground state of hydrogen atom is $0.5 ˚ A$ . The radius of the orbit of the electron in the third excited state of $H e^{+}$ will be

A

8 ˚ A

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B

4 ˚ A

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C

0.5 ˚ A

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D

0.25 ˚ A

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Solution

The correct option is B $4 ˚ A$
Radius, $r \propto \frac{n^{2}}{Z}$

Thus, $\frac{r_{2}}{r_{1}} = \frac{n_{2}^{2} Z_{1}}{n_{1}^{2} Z_{2}} = \frac{4^{2} \times 1}{1^{2} \times 2} = 8$

$\Rightarrow r_{2} = 8 r_{1} = 8 (0.5) = 4 ˚ A$

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