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How do you calculate the frequency of an incident light when given the wavelength and work function (for example: if the wavelength of the ejected electron is 1.1 nm, what was the frequency of the incident light? The work function of sodium is 150.6 kj mol-1)
You would have to find the energy of the incoming photons. You would convert the wavelength of the elected electron into kinetic energy then add that to the work function. This gives you the energy of an incoming photon. Then you simply convert energy into frequency using E=hv
You would first want to convert the nm to m of the ejected electron then utilize the De broglie equation to find velocity of the ejected electron . The velocity you find you then end up putting in the Kenetic Energy Formula= 1/2 mv^2 and add the KE to work function after converting value from KJ to J and dividing the KJ/mol by Avagadro's number if the question states it is one atom of soduim that is being struck with incident light. The last step is to divide your combined energy value (KE+ work function) by planc's constant to get frequency.
Since Kinetic Energy = Initial Energy - Work Function, one could find the frequency of the incoming light by using the De Broglie Equation (Wavelength=Planck's Constant/momentum), you can find the velocity of the ejected electron. Using this velocity in the equation for kinetic energy (E=(1/2)mv^2), you can find the energy of the ejected electron. Then, you add this energy to the work function, granting you the initial energy of the light. Finally, using E=hv and c=v*wavelength, we can make the equation E=ch/wavelength, which can be rewritten as Wavelength=ch/E. We then plug in the calculated value of E and the constants c and h, granting us the wavelength of the initiatory energy.
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