When an electron in a hydrogen atom makes a t | vedclass

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

Question

(A) The frequency of a photon emitted during a transition is given by Rydberg's formula: $f = R c Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

Vedclass · Accepted Answer

$\frac{243}{32}f$

Vedclass · Answer

(A) The frequency of a photon emitted during a transition is given by Rydberg's formula: $f = R c Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.For a hydrogen atom $(Z=1)$,the transition from the $2^{nd}$ excited state $(n_2=3)$ to the ground state $(n_1=1)$ gives frequency $f$:$f = R c (1)^2 \left( \frac{1}{1^2} - \frac{1}{3^2} ight) = R c \left( 1 - \frac{1}{9} ight) = \frac{8}{9} R c$.Thus,$R c = \frac{9}{8} f$.For $Li^{++}$ $(Z=3)$,the transition from the $1^{st}$ excited state $(n_2=2)$ to the ground state $(n_1=1)$ gives frequency $f'$:$f' = R c (3)^2 \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = R c (9) \left( 1 - \frac{1}{4} ight) = R c (9) \left( \frac{3}{4} ight) = \frac{27}{4} R c$.Substituting $R c = \frac{9}{8} f$ into the equation for $f'$:$f' = \frac{27}{4} 	imes \left( \frac{9}{8} f ight) = \frac{243}{32} f$.

When an electron in a hydrogen atom makes a transition from the $2^{nd}$ excited state to the ground state,it emits a photon of frequency $f$. The frequency of the photon emitted when an electron of $Li^{++}$ makes a transition from the $1^{st}$ excited state to the ground state is:

Similar Questions

$A$ particular hydrogen-like ion emits radiation of frequency $2.92 \times 10^{15} \text{ Hz}$ when it makes a transition from $n=3$ to $n=1$. The frequency in $\text{Hz}$ of radiation emitted in the transition from $n=2$ to $n=1$ will be: (in $\times 10^{15}$)

Electrons in a certain energy level $n=n_{1}$ can emit $3$ spectral lines. When they are in another energy level $n=n_{2}$,they can emit $6$ spectral lines. The orbital speed of the electrons in these orbits are in the ratio:

In a hydrogen atom,which quantity is an integral multiple of $\frac{h}{2\pi}$?

Energy required for the electron excitation in $Li^{++}$ from the first to the third Bohr orbit is.....$eV$

$A$ hydrogen-like atom of atomic number $Z$ is in an excited state of quantum number $2n$. It can emit a maximum energy photon of $204 \ eV$. If it makes a transition to quantum state $n$,a photon of energy $40.8 \ eV$ is emitted. The value of $n$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module