What is the ratio of `Deltav==v_("max")-v_("min")` for spectral lines corresponding to lyman `&` Balmer series for hydrogen

Options

A. `27:5`
B. `4:1`
C. `5:4`
D. `9:4`

Answer

D

Explanation

For Lyman series
`barv_("max") = R_H (1/(1^2) - 1/(prop^2)) = R_H`
`barv_("min") = R_H(1/(1^2) - 1/(2^2)) = 3/4 R_H`
`Delta barv_("Lyman") = R_H - 3/4 R_H = (R_H)/4`
For Balmer series
`barv_("max") = R_H(1/(2^2) - 1/(prop^2)) = (R_H)/(4)`
`barv_("min") = R_H(1/(2^2) - 1/(3^2)) = 5/36 R_H`
`Delta barv_("Balmer") = (R_H)/(4) - (5R_H)/(36)`
`= (4R_H)/(36)`
`= (R_H)/(9)`
`(Delta barv_("Lyman"))/(Delta barv_("Balmer")) = (R_H//4)/(R_H//9) = 9/4 " or " 9 : 4`.