Question 6.3: In a photoelectric effect experiment, ultraviolet light with......
In a photoelectric effect experiment, ultraviolet light with a wavelength of 337 nm was directed at the surface of a piece of potassium metal. The kinetic energy of the ejected electrons was measured as 2.30 × 10^{−19} J. What is the electron binding energy for potassium?
Strategy We know that energy must be conserved, and we can use this idea to set up an equation relating the photon energy to the kinetic energy and the binding energy. Because the photon is absorbed in this process, we must be able to account for its energy. Some of that energy does work to overcome the electron binding energy, and the rest appears as the kinetic energy of the ejected electron. We can write this as a simple equation:
E_{\text{photon}} = Binding E + Kinetic E
We know how to find the photon energy from the wavelength, and we know the kinetic energy, so we can solve for the binding energy. As always, we must be careful with the units on all quantities involved.
First find the photon energy.
337\mathrm{~nm}\times\frac{1\,\mathrm{m}}{10^{9}\,\mathrm{nm}}=3.37\times10^{-7}\,\mathrm{m}
E_{\mathrm{photon}}={\frac{h c}{\lambda}}={\frac{(6.626\times10^{-34}\;J\,s)(2.998\times10^{8}\,{\mathrm{m}}\,{\mathrm{s}}^{-1})}{3.37\times10^{-7}{\mathrm{m}}}}=5.89\times10^{-19}\mathrm{~J}
Then use the conservation of energy relationship to find the desired binding energy:
E_{\mathrm{photon}} = Binding E + Kinetic E
So,
Binding E = E_{\text{photon}} − Kinetic E
=\,5.89\times10^{-19}~J-\,2.30\times10^{-19}\mathrm{\;J}=\,3.59\times10^{-19}\mathrm{\;J}
Analyze Your Answer The wavelength used here is slightly shorter than those for visible light, so photon energy in the mid to upper 10^{−19} J range seems reasonable. The binding energy we found is smaller than the photon energy, as it must be. So it appears likely that we have done the calculation correctly.
Check Your Understanding The electron binding energy for chromium metal is 7.21 × 10^{−19} J. Find the maximum kinetic energy at which electrons can be ejected from chromium in a photoelectric effect experiment using light at 266 nm.