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If the radius of the $3 \mathrm{rd}$ Bohr's orbit of hydrogen atom is $r_3$ and the radius of $4^{\text {th }}$ Bohr's orbit is $r_4$. Then:
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$r_4=\frac{16}{9} r_3$
$\begin{aligned} & r=0.529 \times \frac{n^2}{Z} Å \\ & r_3=0.529 \times \frac{3^2}{1} \Rightarrow r_4=0.529 \times \frac{4^2}{1} \\ & \frac{r_4}{r_3}=\frac{4^2}{3^2}=\frac{16}{9} \Rightarrow r_4=\frac{16 r_3}{9}\end{aligned}$
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