The wavelength of `H_(alpha)` line of Balmer series is `6500 Å`. What is the wavelength of `H_(beta)` line of Balmer series?

Answer

4814.8

Explanation

`H_(alpha)` line of Balmer series is obtained when `n_1 = 2,n_2 = 3`
`H_(beta)` line of Balmer series is obtained when `n_1 = 2, n_2 = 4`
Thus, `vecv_(Halpha)=1/(lamda_(Halpha))=R_H(1/2^2-1/3^2)`
`=R_H(1/4-1/16)=R_Hxx3/16" "...(i)`
`vecv_(H_beta)=1/(lamda_(H_beta))=R_H(1/2^2-1/4^2)`
`=R_H(1/4-1/16)=R_Hxx3/16" "...(ii)`
Dividing eqn. (i) by eqn. (iii), we get
`(lamdaH_(beta))/(lamdaH_(alpha))=5/36xx16/3=20/27`
`:. lamda_(H_beta)=20/27 xxlamda_(H_beta)=20/27 xx65000Å=4814.8Å`