Science
Photoelectric Effect Kinetic Energy & Compton X-Ray Wavelength Shift
Calculate a single-photon photoelectric energy threshold and maximum kinetic energy, and separately explore the ideal free-electron Compton wavelength shift.
Keep photoelectric emission and Compton scattering separate
The simple single-photon photoelectric model uses photon energy hc/lambda minus a supplied work function. Here hc is approximated as 1239.84 eV nm. The example work function 4.28 eV is an assumed input; surface condition and material affect actual values.
Below the threshold photon energy, this model reports no single-photon emission rather than assigning kinetic energy to an electron that was not emitted. At threshold it gives the ideal limiting kinetic energy zero. Multiphoton and other emission mechanisms are outside this model.
For emitted electrons, the maximum kinetic energy in eV is numerically equal to the magnitude of the stopping potential in volts. This does not specify the electrode polarity or the current.
The independent Compton example assumes scattering from a free electron initially at rest. It uses the rounded electron Compton wavelength 2.4263 pm and the photon scattering angle, in degrees. The output is a wavelength shift, not the outgoing wavelength; binding effects and moving electrons are outside this calculation.
Maximum photoelectron energy in eV, D2
Valid positive wavelength and work function are required. Values remain unrounded until display.
=IF(COUNT(B2:B3)<>2,"Enter numeric wavelength and work function",IF(OR(B2<=0,B3<=0),"Wavelength and work function must be positive",IF(1239.84/B2<B3,"No single-photon emission",1239.84/B2-B3)))Threshold wavelength in nm, D3
The wavelength must be at or below this ideal threshold for single-photon emission.
=IF(COUNT(B3)<>1,"Enter numeric work function",IF(B3<=0,"Work function must be positive",1239.84/B3))Compton wavelength shift in pm, D4
Forward scattering gives zero shift; backscattering at180 degrees gives twice the rounded Compton wavelength.
=IF(COUNT(B4)<>1,"Enter numeric angle",IF(OR(B4<0,B4>180),"Angle must be between 0 and 180 degrees",2.4263*(1-COS(RADIANS(B4)))))Try the example
Use the original values or change them to test your understanding.