When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons, are emitted with a kinetic energy of 1.68 X 10 5 J mol -1 . What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted? - Wired Faculty

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When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons, are emitted with a kinetic energy of 1.68 X 10⁵ J mol^-1. What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?

Solution

The energy (E) associated with a 300 nm photon is given by
E = hv
$equals space hc over straight lambda space equals space fraction numerator left parenthesis 6.626 space cross times space 10 to the power of negative 34 end exponent Js right parenthesis space left parenthesis 3.0 space cross times 10 to the power of 8 space ms to the power of negative 1 end exponent right parenthesis over denominator 300 space cross times space 10 to the power of negative 19 end exponent straight m end fraction space equals space 6.626 space cross times space 10 to the power of negative 19 end exponent straight J Energy space of space 1 space mole space of space photons space space space equals space 6.626 space cross times 10 to the power of negative 19 end exponent straight J space cross times space 6.022 space cross times space 10 to the power of 23 space mol to the power of negative 1 end exponent space space space equals space 3.99 space cross times space 10 to the power of 5 straight J space mol to the power of negative 1 end exponent$
The minium energy needed to remove a mole of electrons from sodium
$equals space 3.99 space cross times space 10 to the power of 5 straight J space mol to the power of negative 1 end exponent space minus space 1.68 space cross times space 10 to the power of 5 space straight J space mol to the power of negative 1 end exponent space equals space left parenthesis 3.99 space minus 1.68 right parenthesis cross times space 10 to the power of 5 space straight J space mol to the power of negative 1 end exponent space equals space 2.31 space cross times space 10 to the power of 5 straight J space mol to the power of negative 1 end exponent$
The minimum energy for one electron
$equals space fraction numerator 2.31 space cross times space 10 to the power of 5 straight J space mol to the power of negative 1 end exponent over denominator 6.022 space cross times 10 to the power of 23 mol to the power of negative 1 end exponent end fraction space equals space 3.84 space cross times space 10 to the power of negative 19 end exponent straight J space left parenthesis This space corresponds space to space the space wavelength right parenthesis straight lambda space equals space hc over straight E space space space equals fraction numerator left parenthesis 6.626 space cross times space 10 to the power of negative 34 end exponent right parenthesis space cross times space left parenthesis 3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent right parenthesis over denominator 3.84 space cross times space 10 to the power of negative 19 end exponent straight J end fraction space space space space equals 517 space nm left parenthesis This space corresponds space to space green space light right parenthesis.$

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