If , `lambda_(1)` and `lambda_(2)` are the wavelength of the numbers of the Lyman and Paschen seri respectively. Then `lambda_(1):lambda_(2)=`.....

Explanation

Wavelength of first line in Lyman series `lambda_(1)` is,
`:.(1)/(lambda_(1))=R[(1)/(1^(2))-(1)/(n_(i)^(2))] ` [ `:.` for first line `n_(1)=2]`
`:.(1)/(lambda_(1))=R[(1)/(1^(2))-(1)/(r^(2))]=R[1-(1)/(4)]`
`:. (1)/(lambda_(1))=(3R)/(4)....(1)`
`rArr` Wavelength of first line in Paschen series `lambda_(2)`,
`:.(1)/(lambda_(1))=R[(1)/(3^(2))-(1)/(4^(2))] [ :.` for first line `n_(i)=4]`
`:.(1)/(lambda_(2)) [(1)/(9)-(1)/(16)]=R[(7)/(14)]`
`:.(1)/(lambda_(2))=(7R)/(144) ...(2)`
`rArr` Taking ratio of equation (2) and equation (1),
`(lambda_(1))/(lambda_(2))=(7R)/(144)xx(4)/(3R)`
`:. (lambda_(1))/(lambda_(2))=(7)/(108)`