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The frequency of revolution of the electron in the nth Bohr orbit is V_n. What will be the graph between

\log n and \log \frac{V_n}{V_1}?(In the given diagrams \log nis on y-axis and \log \frac{V_n}{V_1}is on x-axis)

Option: 1

Option: 2

Option: 3

Option: 4

Answers (1)


As we know v\propto\frac{Z}{n}

And r\propto\frac{n^2}{Z}

Hence v and r can be written as 

v\ =\frac{C_1Z}{n} and

 r=C_2\frac{n^2}{Z} , where both C1 and C2 are constant 

We know that frequency V_n=\frac{1}{T}=\frac{v}{2\pi r}

Hence V can be written as V_n=cn^{-3}

Now, v_n/v_1=n^{-3}

So \frac{v_n}{v_1}=-3logn

Hence graph between log n  and log\left(\frac{v_n}{v_1}\right)   will be a linear graph with and negative slope passing through the origin.

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