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The wavelength of the first line of Balm...

The wavelength of the first line of Balmer series of H-atom of `6561Å`. The wavelength of the second line of the series is

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For Balamer I line,
`barv_(1)=(1)/(lambda_(1))=R[(1)/(n_(f)^(2))-(1)/(n_(i)^(2))]`
`(1)/(lambda_(1))=R[(1)/(2^(2))-(1)/(3^(2))]=R[(5)/(36)]" "….(1)`
For Balamer II line,
`barv_(2)=(1)/(lambda_(2))=R[(1)/(2^(2))-(1)/(4^(2))]=(3)/(16)R" "....(2)`
Dividing equation (1) by equation (2)
`(lambda_(2))/(lambda_(1))=(R(5//36))/(R(3//16))=(5)/(36)xx(16)/(3)=(20)/(27)`
`(or) lambda_(2)=lambda_(1)((20)/(27))=6563xx (20)/(27)=4861Å`
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