The wavelength of radiation emitted is {lambd | vedclass

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

Question

(B) The Rydberg formula for the wavelength of emitted radiation is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$.F

Vedclass · Accepted Answer

$\frac{20}{27}{\lambda _0}$

Vedclass · Answer

(B) The Rydberg formula for the wavelength of emitted radiation is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.For the transition from $n_2 = 3$ to $n_1 = 2$,the wavelength is ${\lambda _0}$:$\frac{1}{\lambda_0} = R \left[ \frac{1}{2^2} - \frac{1}{3^2} ight] = R \left[ \frac{1}{4} - \frac{1}{9} ight] = R \left[ \frac{9 - 4}{36} ight] = \frac{5R}{36}$.For the transition from $n_2 = 4$ to $n_1 = 2$,let the wavelength be $\lambda$:$\frac{1}{\lambda} = R \left[ \frac{1}{2^2} - \frac{1}{4^2} ight] = R \left[ \frac{1}{4} - \frac{1}{16} ight] = R \left[ \frac{4 - 1}{16} ight] = \frac{3R}{16}$.Dividing the two equations:$\frac{\lambda}{\lambda_0} = \frac{5R/36}{3R/16} = \frac{5}{36} 	imes \frac{16}{3} = \frac{5 	imes 4}{9 	imes 3} = \frac{20}{27}$.Therefore,$\lambda = \frac{20}{27}{\lambda _0}$.

List $I$ (Spectral Lines of Hydrogen for transitions from)	List $II$ (Wavelengths $(nm)$)
$A$. $n_2=3$ to $n_1=2$	$I$. $410.2$
$B$. $n_2=4$ to $n_1=2$	$II$. $434.1$
$C$. $n_2=5$ to $n_1=2$	$III$. $656.3$
$D$. $n_2=6$ to $n_1=2$	$IV$. $486.1$

The wavelength of radiation emitted is ${\lambda _0}$ when an electron jumps from the third to the second orbit of a hydrogen atom. For the electron jump from the fourth to the second orbit of the hydrogen atom,the wavelength of radiation emitted will be

Similar Questions

In the hydrogen spectrum,the ratio of the wavelengths of the last line of the Lyman series and that of the last line of the Balmer series is:

Using the Rydberg formula,calculate the wavelengths of the first four spectral lines in the Lyman series of the hydrogen spectrum.

If $\lambda_1$ is the wavelength of the series limit of the Lyman series,$\lambda_2$ is the wavelength of the first line of the Lyman series,and $\lambda_3$ is the series limit of the Balmer series,then the relation between $\lambda_1, \lambda_2,$ and $\lambda_3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module