Question

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

Answer 1

Correct Answer - D
Lyman series , `n_1=1`
For third line of Lyman series , `n_2=4`
For hydrogen , Z=1
`upsilon_H=c/lambda=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 first line of balmer series , `n_1=2 , n_2 =3`
`upsilon_(Li^(2+)) =c.R_H(1)^2 (1/1-1/(4)^2)=15/16R_H . c`
For lithium, Z=3
For First line of balmer series , `n_1=2, n_2=3`
`upsilon_(Li^(2+))=c. R_H (3)^2 (1/(2)^2 -1/(3)^2)=c. R_Hxx9xx5/36`
`=5/4c. R_H`
`upsilon_H/upsilon_(Li^(2+)) =((15//16)cR_H)/((5//4)cR_H)=15/16xx4/5=3/4`