Radius of a certain orbit of hydrogen atom is 8.48. If energy of electron in this orbit is E/x. then x = ________ (Given a₀ = 0.529, E = energy of electron in ground state). Numerical answer type. Work it out, then open the answer.

Answer: 16. rn = n² a₀ ⇒ n² = (8.48)/(0.529) ≈ 16, so n = 4. En = E/n² = E/16 So x = 16.

Radius of a certain orbit of hydrogen atom is 8.48. If energy of… | JEE Main 2024 (6 Apr, Shift 1)

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Energy of the Electron & Energy Levels

Radius of a certain orbit of hydrogen atom is 8.48 $\text{\AA}$ . If energy of electron in this orbit is $E/x$ . then $x =$ ________ (Given $a_{0} = 0.529\ \text{\AA},\ E =$ energy of electron in ground state).

Numerical answer type. Work it out, then open the answer.

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Answer: 16

$r_n = n^2 a_0 \Rightarrow n^2 = \frac{8.48}{0.529} \approx 16$ , so $n = 4$ .
$E_n = \frac{E}{n^2} = \frac{E}{16}$
So $x = 16$ .

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