1.

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

Answer» `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, `bar(v) H_(alpha) = (1)/(.^(lamda)H_(alpha)) = R_(H) ((1)/(2^(2)) - (1)/(3^(2))) = R_(H) ((1)/(4) - (1)/(9)) = R_(H) xx (5)/(36)` ...(i)
`bar(v) H_(beta) = (1)/(.^(lamda)H_(beta)) = R_(H) ((1)/(2^(2)) - (1)/(4^(2))) = R_(H) ((1)/(4) - (1)/(16)) = R_(H) xx (3)/(16)`..(ii)
Dividing eqn. (i) by eqn. (iii), we get
`(.^(lamda)H_(beta))/(.^(lamda)H_(alpha)) = (5)/(36) xx (16)/(3) = (20)/(27) :. .^(lamda)H_(beta) = (20)/(27) xx .^(lamda)H_(beta) = (20)/(27) xx 6500 Å = 4814.8 Å`


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