Answer:

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...