Question 422: Atoms & Nuclei

Question

In hydrogen atom, the energy of electron in first and third orbit is ' $E_1$ ' and' $E_3$ ' respectively. If $E_3=x E_1$ then the value of $x$ will be

Accepted Answer

For the hydrogen atom,
energy of an electron in the first orbit = $E_1$,
energy of an electron in the third orbit = $E_3$.
If $E_3 = x E_1$, find $x$.
Step 1: Formula for energy in hydrogen atom
$ E_n = - \frac{13.6 \, 	ext{eV}}{n^2} $
So, the energy is inversely proportional to $n^2$.
Step 2: Write $E_1$ and $E_3$
$ E_1 = -\frac{13.6}{1^2} = -13.6 \, 	ext{eV} $
$ E_3 = -\frac{13.6}{3^2} = -\frac{13.6}{9} = \frac{E_1}{9} $
Step 3: Express $E_3$ in terms of $E_1$
$ E_3 = \frac{1}{9} E_1 $
So:
$ x = \frac{1}{9} $
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Answer: Option A $	frac{1}{9}$

Answer

$\frac{1}{9}$

Answer

$\frac{1}{64}$

Answer

$\frac{1}{27}$

Answer

$\frac{1}{8}$

Atoms & Nuclei

In hydrogen atom, the energy of electron in first and third orbit is ' E_1 ' and' E_3 ' respectively. If E_3=x E_1 then the value of x will be

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