When a hydrogen atom emits a photon of energy | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{h}{\pi}$

Vedclass · Answer

(C) The energy of an electron in the $n^{	ext{th}}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} \,eV$.When the atom emits a photon of energy $12.09 \,eV$,the electron jumps from a higher energy level $n_2$ to a lower energy level $n_1$.The energy difference is $\Delta E = E_{n_2} - E_{n_1} = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) = 12.09 \,eV$.Dividing by $13.6$,we get $\frac{1}{n_1^2} - \frac{1}{n_2^2} = \frac{12.09}{13.6} \approx 0.889$.For $n_1 = 1$,we have $1 - \frac{1}{n_2^2} = 0.889$,which gives $\frac{1}{n_2^2} = 0.111$,so $n_2^2 = 9$,implying $n_2 = 3$.Thus,the electron jumps from the $3^{	ext{rd}}$ orbit to the $1^{	ext{st}}$ orbit.The orbital angular momentum is given by $L = \frac{nh}{2\pi}$.The change in angular momentum is $\Delta L = L_2 - L_1 = \frac{n_2 h}{2\pi} - \frac{n_1 h}{2\pi} = \frac{(3-1)h}{2\pi} = \frac{2h}{2\pi} = \frac{h}{\pi}$.

When a hydrogen atom emits a photon of energy $12.09 \,eV$,its orbital angular momentum changes by (where $h$ is Planck's constant)

Similar Questions

As per the Bohr model,the minimum energy (in $eV$) required to remove an electron from the ground state of a doubly ionized $Li$ atom $(Z = 3)$ is:

When the electron jumps from a level $n=4$ to $n=1$,the momentum of the recoiled hydrogen atom will be

Line spectrum was first of all theoretically explained by

In Bohr's atomic model, the energy of the electron is $E$ in the second orbit of a hydrogen atom. The energy of the electron in the third orbit of a helium atom $(Z = 2)$ will be:

It is found experimentally that $13.6 \; eV$ energy is required to separate a hydrogen atom into a proton and an electron. Compute the orbital radius and the velocity of the electron in a hydrogen atom.

Vedclass Test Series

Exam Paper Generator

Online Exam Module