The ratio of the frequency corresponding to the third line in the lyman series of hydrogen atomic spectrum to that of the first line in Balmer series of `Li^(2+)` spectrum is

Options

A. `(4)/(5)`
B. `(5)/(4)`
C. `(4)/(3)`
D. `(3)/(4)`

Answer

D

Explanation

For Lyman series, `n_(1) = 1`. For 3rd line of Lyman series `n_(2) = 4`
For hydrogen, Z = 1. Hence,
`v_(H) = (c)/(lamda) = c R_(H) Z^(2) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`= c R_(H) (1)^(2) ((1)/(1) - (1)/(4^(2))) = (15)/(16) R_(H.c)`
for lithium, Z = 3
For 1st line of Balmer series, `n_(1) = 2, n_(2) = 3`
`:. v_(Li) = c.R_(H) (3)^(2) ((1)/(2^(2)) - (1)/(3^(2)))`
`= c.R_(H) xx 9 xx (5)/(36) =(5)/(4) c.R_(H)`
`:. (v_(H))/(v_(Li)) = ((15//16) c R_(H))/((5//4) c R_(H)) = (15)/(16) xx (4)/(5) = (3)/(4)`