If lambda_1 and lambda_2 are the wavelengths | vedclass

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

Question

(D) Using Rydberg's formula,$\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$.For the first line of the Lyman series,$n_1 = 1$

Vedclass · Accepted Answer

$108: 7$

Vedclass · Answer

(D) Using Rydberg's 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 $n_2 = 2$:$\frac{1}{\lambda_1} = R \left[ \frac{1}{1^2} - \frac{1}{2^2} ight] = R \left[ 1 - \frac{1}{4} ight] = \frac{3R}{4}$.For the first line of the Paschen series,$n_1 = 3$ and $n_2 = 4$:$\frac{1}{\lambda_2} = R \left[ \frac{1}{3^2} - \frac{1}{4^2} ight] = R \left[ \frac{1}{9} - \frac{1}{16} ight] = R \left[ \frac{16 - 9}{144} ight] = \frac{7R}{144}$.Now,calculating the ratio $\frac{\lambda_2}{\lambda_1}$:$\frac{\lambda_2}{\lambda_1} = \frac{1}{\lambda_1} 	imes \lambda_2 = \left( \frac{3R}{4} ight) 	imes \left( \frac{144}{7R} ight) = \frac{3 	imes 36}{7} = \frac{108}{7}$.Thus,$\lambda_2 : \lambda_1 = 108 : 7$.

If $\lambda_1$ and $\lambda_2$ are the wavelengths of the first line of the Lyman and Paschen series respectively,then $\lambda_2 : \lambda_1$ is

Similar Questions

The ratio of the shortest wavelength of the Balmer series to the shortest wavelength of the Lyman series for a hydrogen atom is:

$A$ hydrogen atom in its ground state absorbs a photon and the electron transitions to the $5^{th}$ orbit. When the excited atom returns to its ground state,it emits photons of various energies. What is the maximum number of spectral lines that can be obtained in this process?

If the first line in the Lyman series has wavelength $\lambda$,then the first line in the Balmer series has the wavelength

The wave number of the first line in the Lyman series of a hydrogen atom is ($R$ is Rydberg's constant).

Missing lines in a continuous spectrum reveal

Vedclass Test Series

Exam Paper Generator

Online Exam Module