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Show that Balmer series appears between ...

Show that Balmer series appears between 3647Å and 6563Å in the hydrogen spectrum.

Text Solution

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For Balmer series, `(1)/(lamda)=overline(v)=R[(1)/(2^(2))-(1)/(n^(2))],n=3,4,5, . . .oo`
The limits of Balmer series can be obtained when =3
and n=`oo` respectively.
`(1)/(lamda_("min"))=overline(v)_(max)=R[(1)/(2^(2))-(1)/(oo^(2))]=(R)/(4)=(109678)/(4)cm^(-1)`
`thereforelamda_("min")=(4)/(109678)cm=3647xx10^(-8)cm=3647`Å
Also, `(1)/(lamda_(max))=overliine(v_("min"))=R[(1)/(2^(2))-(1)/(3^(2))]=(5R)/(36)=(5xx109678)/(36)cm^(-1)`
`therefore lamda_(max)=(36)/(5xx109678)=6564xx10^(-8)cm=6564`Å
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