Question

The study of emission line spectra of a material serve as a finger print for identification of the gas.

1. Name different series of lines observed in hydrogen spectrum.

2. Draw energy level diagram of hydrogen atom?

3. Write down the Balmer formula for wavelength of H_α line.

4. Given Rydberg constant as 1.097 × 10⁷ m^-1 . Find the longest and shortest wavelength limit of Baler Series. 

Answer 1

1. Lyman series, Balmer series, Paschen series, Bracket series, P fund series

3. \(\bar v=\frac{1}{λ}=R_H\Big[\frac{1}{n^2_1}-\frac{1}{n^2_2}\Big]\) = \(R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]\)

4.

\(\bar v=\frac{1}{λ}=R_H\Big[\frac{1}{n^2_1}-\frac{1}{n^2_2}\Big]\)

Longest wavelength n₁ = 2 and n₂ = 3

\(\bar v=\frac{1}{λ}=R_H\Big[\frac{1}{n^2_1}-\frac{1}{n^2_2}\Big]\)= \(R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]\)

= 1.097 x 10⁷x \(\frac{5}{36}\)

λ = \(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]}\) = 6563 x 10^-10

= 6563A⁰

Shortest Wavelength n₁ = 2 and n₂ = α

\(\bar v=\frac{1}{λ}=R_H\Big[\frac{1}{n^2_1}\frac{1}{n^2_2}\Big]\) = \(R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]\)

\(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]}\)= \(\frac{1}{1.097\times10^7\Big(\frac{1}{4}\Big)}\)

= 3646 x 10^-10m = 3646 A⁰