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The radius of third stationary orbit of electron for Bohr's atom is $$R$$. The radius of fourth stationary orbit will be:
In Bohr's model, the radius of the $$n$$th orbit is proportional to $$n^2$$:
$$r_n \propto n^2$$
For the third orbit: $$r_3 = R \propto 3^2 = 9$$
For the fourth orbit: $$r_4 \propto 4^2 = 16$$
$$\frac{r_4}{r_3} = \frac{16}{9}$$
$$r_4 = \frac{16}{9}R$$
The answer is $$\frac{16}{9}R$$, which corresponds to Option (2).
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