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  4. In a hydrogen atom, the radius of nth Bohr orbit is rn. The graph between log(rn/r1) and logn will be

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Q. In a hydrogen atom, the radius of $n^{th}$ Bohr orbit is $r_n$. The graph between $log(r_n/r_1)$ and $logn$ will be

Atoms

Solution:

We know that $r_n \propto n^2$ or $(r_n/r_1) = n_2$
So, $log(r_n /r_1) = 2\,log\, n$
Hence, the graph between $log(r_n /r_1)$ and $log\,n$ will be a straight line passing through origin.
The positive slope is given by $tan\,\theta = 2$.