The ratio of the wavelength of the last line | vedclass

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

Question

(A) The wavelength $\lambda$ of a spectral line in the hydrogen atom is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} -

Vedclass · Accepted Answer

$\frac{9}{4}$

Vedclass · Answer

(A) The wavelength $\lambda$ of a spectral line in the hydrogen atom is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$,where $R$ is the Rydberg constant.For the last line of the Paschen series,$n_1 = 3$ and $n_2 = \infty$. Thus,$\frac{1}{\lambda_P} = R \left( \frac{1}{3^2} - \frac{1}{\infty^2} \right) = \frac{R}{9}$,which gives $\lambda_P = \frac{9}{R}$.For the last line of the Balmer series,$n_1 = 2$ and $n_2 = \infty$. Thus,$\frac{1}{\lambda_B} = R \left( \frac{1}{2^2} - \frac{1}{\infty^2} \right) = \frac{R}{4}$,which gives $\lambda_B = \frac{4}{R}$.The ratio of the wavelength of the last line of the Paschen series to that of the Balmer series is $\frac{\lambda_P}{\lambda_B} = \frac{9/R}{4/R} = \frac{9}{4}$.

The ratio of the wavelength of the last line of the Paschen series to that of the Balmer series is:

Similar Questions

The ratio of the shortest wavelengths of Bracket and Balmer series of hydrogen atom is

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

What is the shortest wavelength present in the Paschen series of spectral lines (in $nm$)?

The wavelength of the first line of Balmer series of hydrogen atom is $\lambda$. What will be the wavelength of the same line in doubly ionized lithium?

Taking Rydberg's constant $R_H = 1.097 \times 10^7 \ m^{-1}$,the first and second wavelengths of the Balmer series in the hydrogen spectrum are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module