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

The ratio of the frequency corresponding to the third line in the Lyma

1.	The ratio of the frequency corresponding to the third line in the Lymas series of hydrogen atomic spectrum to that of the first line in Balmer series of Li^(2+) spectrum is
Answer» `(4)/(5)` `(5)/(4)` `(4)/(3)` `(3)/(4)` SOLUTION :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)`