Find the ratio of the first wavelengths of th | vedclass

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

Question

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

Vedclass · Accepted Answer

$5:27$

Vedclass · Answer

(A) The wavelength $\lambda$ for a transition in a hydrogen-like atom is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.For the first line of the Lyman series,$n_1 = 1$ and $n_2 = 2$:$\frac{1}{\lambda_{L_1}} = R \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = R \left( 1 - \frac{1}{4} ight) = \frac{3R}{4} \implies \lambda_{L_1} = \frac{4}{3R}$.For the first line of the Balmer series,$n_1 = 2$ and $n_2 = 3$:$\frac{1}{\lambda_{B_1}} = R \left( \frac{1}{2^2} - \frac{1}{3^2} ight) = R \left( \frac{1}{4} - \frac{1}{9} ight) = R \left( \frac{9-4}{36} ight) = \frac{5R}{36} \implies \lambda_{B_1} = \frac{36}{5R}$.The ratio of the wavelengths is $\frac{\lambda_{L_1}}{\lambda_{B_1}} = \frac{4/3R}{36/5R} = \frac{4}{3} 	imes \frac{5}{36} = \frac{5}{27}$.

Find the ratio of the first wavelengths of the Lyman series and the Balmer series.

Similar Questions

$A$ hydrogen atom absorbs radiation of wavelength $975 \, \mathring{A}$ and transitions from the ground state to an excited state. How many spectral lines are possible in the emission spectrum?

The ratio of the longest to shortest wavelengths in the Brackett series of hydrogen spectra is

$A$ hydrogen atom is excited from the ground state to another state with a principal quantum number equal to $4$. The number of spectral lines in the emission spectra will be:

When the wave of a hydrogen atom comes from infinity into the first orbit,then the value of the wave number is......$cm^{-1}$

In a hydrogen atom,a transition from $n = 4$ to $n = 3$ results in the emission of an infrared photon. Which of the following transitions would also result in the emission of an infrared photon?

Vedclass Test Series

Exam Paper Generator

Online Exam Module