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(C) The frequency of revolution of an electron in the $n^{th}$ Bohr orbit is given by $v_n \propto \frac{1}{n^3}$.Therefore,$v_n = \frac{k}{n^3}$ for

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(C) The frequency of revolution of an electron in the $n^{th}$ Bohr orbit is given by $v_n \propto \frac{1}{n^3}$.Therefore,$v_n = \frac{k}{n^3}$ for some constant $k$.For the first orbit $(n=1)$,$v_1 = k$.Thus,the ratio is $\frac{v_n}{v_1} = \frac{k/n^3}{k} = \frac{1}{n^3} = n^{-3}$.Taking the logarithm on both sides,we get $\log (v_n / v_1) = \log (n^{-3}) = -3 \log n$.This equation is of the form $y = mx$,where $y = \log (v_n / v_1)$,$x = \log n$,and the slope $m = -3$.Since the slope is negative,the graph is a straight line passing through the origin with a negative slope.

The frequency of revolution of an electron in the $n^{th}$ Bohr orbit is $v_n$. The graph between $\log n$ and $\log (v_n / v_1)$ may be

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