Photoelectric Effect Calculator Formula

Understand the math behind the photoelectric effect calculator. Each variable explained with a worked example.

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Formulas Used

Photon Energy

photon_energy = 6.626e-34 * 299792458 / (wavelength_nm * 1e-9) / 1.602e-19

Max Kinetic Energy

ke_max = 6.626e-34 * 299792458 / (wavelength_nm * 1e-9) / 1.602e-19 - work_function

Threshold Wavelength

threshold_wavelength = 6.626e-34 * 299792458 / (work_function * 1.602e-19) * 1e9

Variables

VariableDescriptionDefault
wavelength_nmPhoton Wavelength(nm)250
work_functionWork Function(eV)2.3

How It Works

Photoelectric Effect

Einstein explained that light consists of photons, each carrying energy E = hf. When a photon hits a metal surface, it can eject an electron if its energy exceeds the work function.

Formula

KE_max = hf - phi = (hc/lambda) - phi

where phi is the work function (minimum energy to free an electron). The threshold wavelength is lambda_0 = hc/phi.

Worked Example

UV light at 250 nm hitting sodium (work function = 2.3 eV).

wavelength_nm = 250work_function = 2.3
  1. 01E_photon = hc/lambda = (6.626e-34 * 3e8) / (250e-9)
  2. 02E_photon = 7.95e-19 J = 4.96 eV
  3. 03KE_max = E_photon - phi = 4.96 - 2.3
  4. 04KE_max = 2.66 eV
  5. 05Threshold: lambda_0 = hc/phi = 1240/2.3 = 539.1 nm

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