Ratio of longest wavelength corresponding to | vedclass

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

Question

(C) The Rydberg formula for the hydrogen spectrum is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$.For the Lyman s

Vedclass · Accepted Answer

$\frac{5}{27}$

Vedclass · Answer

(C) The Rydberg formula for the hydrogen spectrum is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.For the Lyman series,$n_1 = 1$. The longest wavelength corresponds to the smallest energy transition,which occurs at $n_2 = 2$.$\frac{1}{\lambda_{\max(L)}} = R \left[ \frac{1}{1^2} - \frac{1}{2^2} ight] = R \left[ 1 - \frac{1}{4} ight] = \frac{3R}{4} \implies \lambda_{\max(L)} = \frac{4}{3R}$.For the Balmer series,$n_1 = 2$. The longest wavelength corresponds to the smallest energy transition,which occurs at $n_2 = 3$.$\frac{1}{\lambda_{\max(B)}} = R \left[ \frac{1}{2^2} - \frac{1}{3^2} ight] = R \left[ \frac{1}{4} - \frac{1}{9} ight] = R \left[ \frac{9-4}{36} ight] = \frac{5R}{36} \implies \lambda_{\max(B)} = \frac{36}{5R}$.The ratio of the longest wavelengths is $\frac{\lambda_{\max(L)}}{\lambda_{\max(B)}} = \frac{4}{3R} 	imes \frac{5R}{36} = \frac{4 	imes 5}{3 	imes 36} = \frac{20}{108} = \frac{5}{27}$.

Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

Similar Questions

The shortest wavelength in the Lyman series is $91.2 \, nm$. The largest wavelength of the series is.....$nm$

In the hydrogen emission spectrum,for any series,the principal quantum number of the higher energy level is $n+1$ and the lower energy level is $n$. The corresponding maximum wavelength $\lambda$ is ($R=$ Rydberg's constant).

The ratio of the largest to shortest wavelengths in the Lyman series of hydrogen spectra is

The extreme wavelengths of the Paschen series are

The shortest wavelength in the Balmer series of a hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen-like atom of atomic number $Z$. The value of $Z$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module