The wavelength of the first spectral line of | 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 spectral lines is given by $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) Z^2$.

Vedclass · Accepted Answer

$1215 \mathring A$

Vedclass · Answer

(B) The Rydberg formula for the wavelength of spectral lines is given by $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) Z^2$.For the Lyman series,the electron transitions to the ground state,so $n_1 = 1$.The first spectral line of the Lyman series corresponds to the transition from the first excited state to the ground state,so $n_2 = 2$.For hydrogen,the atomic number $Z = 1$.Substituting these values into the formula:$\frac{1}{\lambda} = R \left( \frac{1}{1^2} - \frac{1}{2^2} ight) (1)^2 = R \left( 1 - \frac{1}{4} ight) = R \left( \frac{3}{4} ight)$.Therefore,$\lambda = \frac{4}{3R}$.Given that $\frac{1}{R} \approx 911.6 \mathring A$ (often approximated as $912 \mathring A$),we have:$\lambda = \frac{4}{3} 	imes 911.6 \mathring A \approx 1215.5 \mathring A$.Rounding to the nearest option,the wavelength is $1215 \mathring A$.

The wavelength of the first spectral line of the Lyman series of the hydrogen spectrum is

Similar Questions

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).

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is :-

The ratio of the longest to the shortest wavelength emitted in the Paschen series of a hydrogen atom is:

The spectral series of the hydrogen spectrum that lies in the ultraviolet region is the

The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module