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If an electron is revolving in its Bohr orbit having Bohr radius of $0.529 Å$, then the radius of third orbit is
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Verified Answer
The correct answer is:
$4.761 Å$
Given, Bohr radius, $r_1=0.529 Å$
We know that, radius of revolving electron in $n$th orbit is given as
$$
r \propto n^2
$$
$$
\begin{array}{ll}
\Rightarrow & r_1=\left(\begin{array}{l}
n_1 \\
n_2
\end{array}\right)^2 \\
\Rightarrow & \frac{r_1}{r_2}=\left(\frac{1}{3}\right)^2=\frac{1}{9} \quad\left[\because n_1=1 \text { and } n_2=3\right] \\
\Rightarrow & r_2=9 r_1=9 \times 0.529=4.761 Å
\end{array}
$$
We know that, radius of revolving electron in $n$th orbit is given as
$$
r \propto n^2
$$
$$
\begin{array}{ll}
\Rightarrow & r_1=\left(\begin{array}{l}
n_1 \\
n_2
\end{array}\right)^2 \\
\Rightarrow & \frac{r_1}{r_2}=\left(\frac{1}{3}\right)^2=\frac{1}{9} \quad\left[\because n_1=1 \text { and } n_2=3\right] \\
\Rightarrow & r_2=9 r_1=9 \times 0.529=4.761 Å
\end{array}
$$
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