The ratio of the wavelengths for 2 to 1 trans | vedclass

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

Question

(C) The Rydberg formula for the wavelength $\lambda$ of a transition between energy levels $n_2$ and $n_1$ is given by $\frac{1}{\lambda} = R Z^2 \lef

Vedclass · Accepted Answer

$4:9:36$

Vedclass · Answer

(C) The Rydberg formula for the wavelength $\lambda$ of a transition between energy levels $n_2$ and $n_1$ is given by $\frac{1}{\lambda} = R Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.Since the transition $2 	o 1$ is the same for all three,the term $\left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$ is constant.Therefore,$\lambda \propto \frac{1}{Z^2}$.For $Li^{++}$,$Z = 3$,so $\lambda_{Li^{++}} \propto \frac{1}{3^2} = \frac{1}{9}$.For $He^{+}$,$Z = 2$,so $\lambda_{He^{+}} \propto \frac{1}{2^2} = \frac{1}{4}$.For $H$,$Z = 1$,so $\lambda_{H} \propto \frac{1}{1^2} = \frac{1}{1}$.Thus,$\lambda_{Li^{++}} : \lambda_{He^{+}} : \lambda_{H} = \frac{1}{9} : \frac{1}{4} : 1$.Multiplying by $36$,we get $4 : 9 : 36$.

The ratio of the wavelengths for $2 \to 1$ transition in $Li^{++}, He^{+}$ and $H$ is

Similar Questions

Which of the plots shown in the figure represents speed $(v)$ of the electron in a hydrogen atom as a function of the principal quantum number $(n)$?

According to de Broglie,if the wavelength of an electron in the second orbit is $10^{-9} \ m$,then the circumference of the orbit is .......

Assertion : Bohr had to postulate that the electrons in stationary orbits around the nucleus do not radiate.
Reason : According to classical physics all moving electrons radiate.

In a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?

The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is proportional to ($e$ = electronic charge).

Vedclass Test Series

Exam Paper Generator

Online Exam Module