Question

The ratio of difference in wavelength of 1st and 2nd lines of lyman series in H-like atom to difference in wavelength for 2nd and 3rd line of same series is:-

Answer 1

Hii dear,

# Answer- 25:7

# Explaination-
Wavelength in lyman series is given by
λ = R(1-1/n^2)

For 1st line, n=2
λ1 = R(1-1/4)
λ1 = 4/3R

For 2nd line, n=3
λ2 = R(1-1/9)
λ2 = 9/8R

For 3rd line, n=4
λ3 = R(1-1/16)
λ3 = 16/15R

Now,
λ1-λ2 = 4/3R - 9/8R = 5/24R ...(1)
λ2-λ3 = 9/8R - 16/15R = 7/120R ...(2)

Dividing (1) by (2)
(λ1-λ2)/(λ2-λ3) = 25/7 = 3.57

Ratio (λ1-λ2) : (λ2-λ3) = 25 : 7

Hope this is helpful...