From Bohr's energy quantization formula, determine the largest wavelength in the Balmer series of hydrogen atom spectrum.

From the Bohr’s energy equation,

straight E space equals space minus 1 half fraction numerator Ze squared over denominator 4 πε subscript straight o rη end fraction space equals space fraction numerator negative Ze squared over denominator 8 πε subscript straight o straight eta squared straight r end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis

The wave number of radiation emitted by such as ion transition from n_i to n_f is given by,

straight nu with bar on top space space equals space 1 over lambda space equals space Z squared space R space open parentheses 1 over n subscript f squared space minus space 1 over n subscript i squared close parentheses

For Balmer Series :

n_i = 3

n_f = 2

$fraction numerator 1 over denominator straight lambda subscript max space end fraction space equals space space R space open square brackets 1 over 2 squared space minus space 1 over 3 squared close square brackets fraction numerator 1 over denominator straight lambda subscript max space end fraction space equals space open square brackets fraction numerator 5 R over denominator 4 space x space 9 space end fraction close square brackets fraction numerator 1 over denominator straight lambda subscript max space end fraction space equals space fraction numerator 5 space x space 1.097 space x space 10 to the power of 7 over denominator 4 space x space 9 space end fraction straight lambda subscript max space equals space fraction numerator 4 space straight x space 9 over denominator 5 space x space 1.097 space x space 10 to the power of 7 end fraction space equals space 656 space straight x space 10 to the power of negative 9 end exponent space straight m$

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