Question

What are frequency and wavelength of a photon emitted during a transition from n=5 state to n = 2 state in hydrogen atom?

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Solution

because space space increment straight E space equals 2.18 space cross times space 10 to the power of negative 18 end exponent straight J 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

As n₁= 2 and n₂ = 5, this transition gives rise to a spectral line in the Balmer series.

increment straight E space equals 2.18 space cross times space 10 to the power of negative 18 end exponent straight J space open square brackets 1 over 2 squared minus 1 over 5 squared close square brackets space space space space space space equals 2.18 space cross times 10 to the power of negative 18 end exponent straight J open square brackets 1 fourth minus 1 over 25 close square brackets space space space space space space equals 4.58 space cross times 10 to the power of negative 19 end exponent straight J

Also comma space increment straight E space equals space hv or space space space space space straight v space equals space fraction numerator increment straight E over denominator straight h end fraction therefore space space space space straight v space equals space fraction numerator 4.58 space cross times space 10 to the power of negative 19 end exponent straight J over denominator 6.62 space cross times 10 to the power of negative 34 end exponent Js end fraction space space space space space space space space space space equals space 6.91 space cross times 10 to the power of 14 straight s to the power of negative 1 end exponent Also comma space space space straight lambda space equals straight c over straight lambda space equals space fraction numerator 3.0 space cross times 10 to the power of 8 space ms to the power of negative 1 end exponent over denominator 6.91 space cross times 10 to the power of 14 straight s to the power of negative 1 end exponent end fraction space space space space space space space space space space space space space space equals space 434 space cross times space 10 to the power of negative 9 end exponent straight m space space space space space space space space space space space space space space equals space 434 space nm

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