With the increase in principal quantum number | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$.The energy difference between

Vedclass · Accepted Answer

Decreases

Vedclass · Answer

(B) The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$.The energy difference between two successive levels $n$ and $n+1$ is $\Delta E = E_{n+1} - E_n = -13.6 \left( \frac{1}{(n+1)^2} - \frac{1}{n^2} ight) = 13.6 \left( \frac{1}{n^2} - \frac{1}{(n+1)^2} ight) = 13.6 \left( \frac{(n+1)^2 - n^2}{n^2(n+1)^2} ight) = 13.6 \left( \frac{2n+1}{n^2(n+1)^2} ight)$.As the principal quantum number $n$ increases,the denominator $n^2(n+1)^2$ increases much faster than the numerator $(2n+1)$.Therefore,the energy difference $\Delta E$ decreases as $n$ increases.From the provided image,we can see that the energy gap between levels decreases as we move to higher energy states: $E_1 > E_2 > E_3$.

With the increase in principal quantum number,the energy difference between two successive energy levels

Similar Questions

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \frac{\lambda_1}{\lambda_2}$ is given by

What is the ratio of the total energy of an electron in a hydrogen atom in the first excited state to that in the third excited state?

An electron with kinetic energy $E$ collides with a hydrogen atom in the ground state. The collision will be elastic

Energy of an electron in $n^{th}$ orbit of hydrogen atom is $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

The energy $E$ of a hydrogen atom with principal quantum number $n$ is given by $E = \frac{-13.6}{n^2} \; eV$. The energy of a photon emitted when the electron jumps from the $n = 3$ state to the $n = 2$ state of hydrogen is approximately......$eV$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module