Rydberg formula question

Question

Using the Rydberg formula, find the wavelength of the line in the Balmer series of the hydrogen spectrum for m = 3. The value of Rydberg constant is 1.097 × 10⁷ m^–1 and n = 2 for the Balmer series.

Answer 1

Rydberg formula for hydrogen atoms is 1/λ = R[ 1/n_f² - 1/n_i² ] = (1.097 x 10⁷) [ 1/2² - 1/3² = 0.13889 ], λ = 1 / (0.15236 x 10⁷) = 6.563 x 10^-7 m = 656.3 nm.