Q161 / 180 · KCET 2024 · Physics

The ratio of area of first excited state to ground state of orbit of hydrogen atom'is

A
$1: 16$
B
$1: 4$
C
$4: 1$
Correct answer
D
$16: 1$

Solution

Since, $r_n \propto n^2$ $\therefore$ Area, $A_n \propto r_n^2 \propto n^4$ $\Rightarrow \quad \frac{A_{n_1}}{A_{n_2}}=\left(\frac{n_1}{n_2}\right)^4=\left(\frac{2 n}{n}\right)^4=16$ $\therefore \quad A_{n_1}: A_{n_2}=16: 1$

Hence, the correct answer is option: 'D'.

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