Let λ1 be largest wavelength of Lyman series for hydrogen atom and λ2 be largest wavelength of Balmer series

Question

Let \(\lambda _1\) be largest wavelength of Lyman series for hydrogen atom and \(\lambda _2\) be largest wavelength of Balmer series then \(\frac{\lambda _1}{\lambda _2}\) is

(1) \(\frac{5}{27}\)

(2) \(\frac{1}{4}\)

(3) \(\frac{3}{4}\)

(4) \(\frac{4}{9}\)

Answer 1

Correct option is : (1) \(\frac{5}{27}\)

\(\frac{1}{\lambda} = Rz^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2}\right)\)

\(\frac{1}{\lambda _1} = Rz^2\left( \frac{1}{1}- \frac{1}{4}\right)\)

\(\frac{1}{\lambda _2} = Rz^2 \left( \frac{1}{4} - \frac{1}{9}\right)\)

\(\frac{\lambda _1}{\lambda _2} = \frac{5}{27}\)