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

The magnetic moment $(\mu)$ of an electron revolving around the nucleus varies with the principal quantum number $n$ as

When an electron in a Hydrogen atom revolves in a stationary orbit,it

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy $2.86 \ eV$. The integer value of $n$ will be . . . . . . .

An electron in the $n = 1$ orbit of a hydrogen atom is bound by $13.6\, eV$. The energy required to ionize it is........$ eV$.

What is the radius of an iodine atom (atomic number $53$,mass number $126$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module