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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 $\log n$ is on y-axis and $\log \frac{V_n}{V_1}$ is on x-axis)
Option: 1

Option: 2

Option: 3

Option: 4

Answers (1)

best_answer

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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Gaurav

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