Calculate the wavenumber for radiation of longest wavelength in Balmer series of atomic hydrogen.

Explanation

In Balmer series, longest wavelength is possible when electron will come back from 3rd energy shell to 2nd energy shell.
Longest wavelength line can be calculated by the following relation:
`vecv = (1)/(lamda ) = R _(H) [ (1)/( n _(1) ^(2)) - (1)/( n _(2) ^(2)) ] cm ^(-1) [ R _(H) = 109, 677 cm ^(-1) ]`
Here `n _(1) =2` is second energy shell.
`n _(2) = 3` is third energy shell.
Bt putting all these vlaues in equation (i), we have
`vec v = 109, 677 [ (1)/( 2 ^(2)) - (1)/( 3 ^(2)) ] cm ^(-1) = 109, 677 [ (1)/(4)- (1)/(9) ] cm ^(-1)`
`= 109, 677 xx (5)/(36) cm ^(-1)`
`vec = 1. 523 xx 10 ^(4) cm ^(-1) = 1. 523 xx 10 ^(6) m ^(-1)`