Calculate the wavelength from the Balmer formula when n₂ = 3.

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Solution

According to Balmer formula,

straight v with bar on top space equals space 109677 space open square brackets fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close square brackets space cm to the power of negative 1 end exponent

where space straight n subscript 1 space equals space 2 comma space space space straight n subscript 2 space equals space 3 space for space Balmer space series

straight v with bar on top space equals space 109677 space open square brackets fraction numerator 1 over denominator left parenthesis 2 right parenthesis squared end fraction minus fraction numerator 1 over denominator left parenthesis 3 right parenthesis squared end fraction close square brackets space cm to the power of negative 1 end exponent space space space equals space 109677 open square brackets 1 fourth minus 1 over 9 close square brackets cm to the power of negative 1 end exponent space space space equals space fraction numerator 109677 space cross times space 5 over denominator 36 end fraction cm to the power of negative 1 end exponent therefore space space space space space space space space space space straight lambda space equals 1 over straight v space space space space space space space space space space space space space space space equals space fraction numerator 36 over denominator 109677 space cross times space 5 end fraction cm space space space space space space space space space space space space space space space equals space 6.57 space cross times space 10 to the power of negative 5 end exponent cm space space space space space space space space space space space space space space space equals space space fraction numerator 36 over denominator 109677 space cross times 5 end fraction cross times 10 to the power of negative 7 end exponent space mm space space space space space space space space space

= 656 nm

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