Question

The longest weavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

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Solution

Here space straight lambda subscript 1 space equals 589 space nm space equals space 589 space cross times space 10 to the power of negative 9 end exponent straight m space space space space space space space space straight lambda subscript 2 space equals space 589.6 space nm space equals space 589.6 space cross times space 10 to the power of negative 9 end exponent straight m We space know comma space straight v space equals straight c over straight lambda

therefore space space straight v subscript 1 space equals space straight c over straight lambda subscript 1 space equals space fraction numerator 3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent over denominator 589 space cross times 10 to the power of negative 9 end exponent straight m end fraction space equals space 5.093 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent or space space straight v subscript 2 space equals space straight c over straight lambda subscript 2 space equals space fraction numerator 3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent over denominator 589.6 cross times 10 to the power of negative 9 end exponent straight m end fraction space equals space 5.088 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent space space space space Also space increment straight E space equals space straight E subscript 2 minus straight E subscript 1 space equals hv subscript 2 space minus space hv subscript 1 space equals space straight h left parenthesis straight v subscript 2 minus straight v subscript 1 right parenthesis space space space space space or space space space increment straight E space equals space left parenthesis 6.22 space cross times space 10 to the power of negative 34 end exponent Js right parenthesis space open square brackets 5.093 minus 5.088 close square brackets cross times 10 to the power of 14 straight s to the power of negative 1 end exponent space space space space space space space space space space space space space space equals space 3.31 space cross times space 10 to the power of negative 22 end exponent straight J space

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Structure Of Atom

The longest weavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

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