Question

calculate the wavelength of the second line of lyman series in hydrogen spectra (given RH =1.09737 c /M)

Answer 1

We have formula , $\bold{\frac{1}{\lambda}=RZ^2[\frac{1}{n_i^2} - \frac{1}{n_f^2}]}$
Here λ is wavelength , R is Rydberg constant i.e., Rh = 109737 cm⁻¹
For Lyman series ni = 1 and nf = 2, 3, 4, ....... ∞
But question is saying about 2nd line of Lyman series
means , ni = 1 and nf = 3

So, 1/λ = 109737 cm⁻¹ × (1)² [ 1/1² - 1/3² ] [ for Hydrogen Spectra Z = 1 ]
= 109737 × [1 - 1/9 ]
= 109737 × 8/9 cm⁻¹
= 877896/9cm⁻¹

Now, λ = 9/877896 cm = 1.025 × 10⁻⁷ m = 102.5 nm