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Calculate the wave number for the second line and limiting line of hydrogen atom if the first line appears at 456 nm in the calmer series

Asked by bhavya.vashisth8 19th August 2018, 7:16 PM
Answered by Expert
Answer:
The wave number for the second line and limiting line of H- atom of Balmer series is:
 
For Balmer series;
 
straight nu with minus on top space equals straight R space open square brackets fraction numerator 1 over denominator begin display style open parentheses 2 close parentheses squared end style end fraction minus fraction numerator 1 over denominator begin display style open parentheses straight n subscript 2 close parentheses squared end style end fraction close square brackets

For space second space line comma

straight n subscript 1 space equals 2 space comma space straight n subscript 2 space equals 4

straight nu with minus on top space equals straight R open square brackets fraction numerator begin display style 1 end style over denominator begin display style open parentheses 2 close parentheses squared end style end fraction minus fraction numerator 1 over denominator begin display style open parentheses 4 close parentheses squared end style end fraction close square brackets

space space space equals 109677 open square brackets 1 fourth minus 1 over 16 close square brackets

space space space equals 109677 open parentheses 0.1875 close parentheses

straight nu with minus on top space equals 20564.43 space cm to the power of negative 1 end exponent

For space limiting space line comma

straight n subscript 1 space equals 2 space comma space straight n subscript 2 space equals infinity

straight nu with minus on top space equals straight R open square brackets fraction numerator begin display style 1 end style over denominator begin display style open parentheses 2 close parentheses squared end style end fraction minus fraction numerator 1 over denominator begin display style open parentheses infinity close parentheses squared end style end fraction close square brackets

space space space equals 109677 open square brackets fraction numerator begin display style 1 end style over denominator begin display style 4 end style end fraction minus 0 close square brackets

straight nu with minus on top space equals 27419.25 space cm to the power of negative 1 end exponent
The wave number for the second line of H- atom of Balmer series is 20564.43 cm-1 and for limiting line is 27419 cm-1.
Answered by Expert 21st August 2018, 1:33 PM
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