Given Rydberg constant as 1.097 × 10-7 m . Find the longest and short

1.	Given Rydberg constant as 1.097 × 10-7 m . Find the longest and shortest wavelength limit of Baler Series.
Answer» \(\bar v=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) Longest wavelength n₁ = 2 and n₂ = 3 \(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) \(R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]\) λ = \(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{3^3}\Big]}\) = 6563 A⁰ Shortest Wavelength n₁ = 2 and n₂ = α \(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) = \(R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]\) λ =\(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]}\) = \(\frac{1}{1.097\times10^7\Big(\frac{1}{4}\Big)}\) = 3646 A⁰

Given Rydberg constant as 1.097 × 10-7 m . Find the longest and shortest wavelength limit of Baler Series.

Answer»

\(\bar v=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\)

Longest wavelength n₁ = 2 and n₂ = 3

\(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) \(R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]\)

λ = \(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{3^3}\Big]}\) = 6563 A⁰

Shortest Wavelength n₁ = 2 and n₂ = α

\(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) = \(R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]\)

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

= 3646 A⁰