Structure of Atom

Structure of Atom

Question

The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097×107 m-1)

  • 91 nm

  • 9.1×10-8 nm

  • 406 nm

  • 192 nm

Answer

A.

91 nm

1 over straight lambda space equals space top enclose straight V subscript straight H space equals space top enclose straight R subscript straight H end enclose 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 equals space 1.097 space straight x space 10 to the power of 7 space open square brackets 1 over 1 squared minus 1 over infinity close square brackets
therefore space straight lambda space equals space fraction numerator 1 over denominator 1.097 space straight x space 10 to the power of 7 end fraction space straight m space equals space 9.11 space straight x space 10 to the power of negative 8 end exponent space straight m
space equals space 91.1 space straight x space 10 to the power of negative 9 end exponent space straight m space equals space 91.1 space nm space left parenthesis 1 nm space equals space 10 to the power of negative 9 end exponent space straight m right parenthesis

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