Question

What is the wavelength of ligh emitted when the election in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2?

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Solution

because space space increment straight E space equals space 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 Here space straight n subscript 1 space equals 2 semicolon space space space straight n subscript 2 space equals 4 therefore space space space space space increment straight E space equals space 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 4 squared close square brackets space space space space space space space space 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 16 close square brackets space space space space space space space space space space space space space space equals space 4.09 space cross times space 10 to the power of negative 19 end exponent straight J

Also comma space space space increment straight E space equals space hv space equals space hc over straight lambda therefore space space space space space space space straight lambda space equals space fraction numerator hc over denominator increment straight E end fraction space space space space space space space space space space space space space equals fraction numerator left parenthesis 6.62 space cross times space 10 to the power of negative 34 end exponent Js right parenthesis space cross times left parenthesis 3 space cross times space 10 to the power of 8 ms to the power of negative 1 end exponent right parenthesis over denominator 4.09 space cross times space 10 to the power of negative 19 end exponent straight J end fraction equals space 4.86 space cross times space 10 to the power of negative 7 end exponent straight m equals space 486 space cross times 10 to the power of negative 9 end exponent straight m equals space 486 space nm

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