If in hydrogen atom, radius of $n^{t h}$ Bohr orbit is $r_{n},$ frequency of revolution of electron in $n^{t h}$ orbit is $f_{n}$ and area enclosed by $n^{t h}$ orbit $A_{n},$ which of the following graph is/are correct?

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Solution

The correct options are
A
B
From Bohr's atomic theory,
(A) $r_{n} \propto \frac{n^{2}}{Z}$
so graph of $r_{n}$ and $n$ will be parabolic.

(B) $\frac{A_{n}}{A_{1}} = \frac{r_{n}^{2}}{r^{2}} = \frac{n^{4}}{1}$
$l o g \frac{A_{n}}{A_{1}} = 4 l o g n$
comparing with $y = m x + c$ , the graph will be straight line starting from origin.

(C) $r_{n} \propto n^{2}$ or $r_{n} = k n^{2}$ where $k$ is some proportionality constant.
$l o g r_{n} = 2 l o g n + l o g k$
so it will be a straight line but not starting from origin.

(D) frequency $(f) \propto \frac{z^{2}}{n^{3}}$
$\frac{f_{n}}{f_{1}} = \frac{1}{n^{3}}$
$l o g (\frac{f_{n}}{f_{1}}) = l o g 1 - 3 l o g n$
$l o g (\frac{f_{n}}{f_{1}}) = - 3 l o g n$
so, it will be a straight line but with negative slope.

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If in hydrogen atom, radius of nth Bohr orbit is rn, frequency of revolution of electron in nth orbit is fn and area enclosed by nth orbit An, which of the following graph is/are correct?

If in hydrogen atom, radius of $n^{t h}$ Bohr orbit is $r_{n},$ frequency of revolution of electron in $n^{t h}$ orbit is $f_{n}$ and area enclosed by $n^{t h}$ orbit $A_{n},$ which of the following graph is/are correct?