Photoelectric Effect Calculator - hf minus phi in nine metals

A photoelectric effect calculator takes the wavelength of an incoming photon and the work function of a metal, then returns photon energy, maximum kinetic energy K_max, stopping potential, electron speed, threshold frequency, and cutoff wavelength from Einstein's 1905 equation.

• • Modern physics homework: Solve textbook problems asking for K_max or V_s for a given wavelength and metal such as sodium, cesium, or copper without re-deriving the constants each time.
• • AP Physics C and quantum physics labs: Verify the linear K_max-vs-frequency graph and back the work function out of the x-intercept using the same NIST CODATA constants the textbook uses.
• • Photodetector and solar cell design: Pick the longest wavelength a metal will respond to (cutoff wavelength) or compare alkali metals with low work functions for low-light photodetectors.
• • Photoelectron spectroscopy calibration: Check the stopping potential you would read off a real photoelectron spectrum against the theoretical prediction before trusting the experimental value.

Wavelengths above the cutoff wavelength lambda_c for a given metal leave the photon energy below the work function phi, so no photoelectron is emitted at all.

Once you know the electron Compton wavelength from Compton Wavelength Calculator, the photoelectric effect is the next step, because both experiments probe the same h c pair but on different kinematic setups.

The photoelectric effect calculator converts wavelength to photon energy with E = h c / lambda, then subtracts the work function phi from the selected metal. If the remainder is positive it becomes the maximum kinetic energy K_max, and every other output follows from that one number.

• wavelength: Wavelength of the incoming photon in nm, converted to meters as lambda_m = lambda_nm * 1e-9.
• material: Selected metal; the work function phi is read from a built-in table sourced from NIST CODATA and the standard work function table.
• Photon energy: Output in eV equal to h c / lambda, also equal to h f where f = c / lambda.
• Max kinetic energy K_max: Output in eV equal to h f - phi when the photon has enough energy, else 0.
• Stopping potential V_s: Output in volts equal to K_max / e, the bias that just stops the most energetic photoelectron.
• Max electron speed: Output in m/s computed from K_max = (1/2) m_e v^2.
• Threshold frequency f0: Output in PHz equal to phi / h; the lowest frequency that releases an electron.
• Cutoff wavelength lambda_c: Output in nm equal to c / f0; the longest wavelength that still releases an electron.

If the photon energy is less than or equal to the work function the calculator reports zero kinetic energy and zero stopping potential and surfaces a clear 'no electron emitted' indicator, because the Einstein equation forbids a negative K_max.

According to Wikipedia - Photoelectric effect, Einstein's 1905 equation K_max = h f - phi gives the maximum kinetic energy of a photoelectron in terms of the photon frequency f and the metal's work function phi.

When the photon does not eject the electron but scatters off it instead, Compton Scattering Calculator takes the same h and c and returns the wavelength shift and recoil energy for any scattering angle.

Four ideas drive every output of the photoelectric effect calculator: the photon energy from h c / lambda, the work function, the Einstein equation K_max = h f - phi, and the threshold frequency that follows from it.

For the atomic side of the same quantum story, Bohr Model Calculator returns the hydrogen-like transition wavelengths that show up when an atom absorbs or emits a photon of a specific energy.

Enter a wavelength, pick the metal whose work function you want to use, and read the seven outputs in the right-hand panel. The page recalculates as you type, so you can compare metals at a single wavelength by clicking the selector.

1. 1 Enter the wavelength: Type the wavelength of the incoming photon in nm, between 1 nm and 2000 nm.
2. 2 Pick the metal: Choose a metal from the dropdown. The work function phi is loaded automatically from the NIST CODATA work function table.
3. 3 Read the photon energy: The first output is the photon energy in eV. For 400 nm it reads about 3.10 eV; for 700 nm about 1.77 eV. If this is below phi, no photoelectron is emitted.
4. 4 Read K_max: The K_max output is in eV. It equals photon energy minus phi above threshold, and is exactly 0 below threshold.
5. 5 Compare the stopping potential: The stopping potential in volts equals K_max in eV, the bias that brings the most energetic electron to rest.
6. 6 Inspect the speed and threshold data: The max speed in m/s comes from K_max = (1/2) m_e v^2; the threshold frequency in PHz and cutoff wavelength in nm describe the metal, not the chosen wavelength.

Switch the metal from sodium to cesium at 500 nm. K_max climbs from 0.12 eV (Na, phi = 2.36 eV) to 0.38 eV (Cs, phi = 2.10 eV) and V_s climbs the same. The threshold frequency falls from 5.71 PHz to 5.08 PHz, and the cutoff wavelength grows from 525 nm to 590 nm.

When the photon you are shooting at the metal has an energy that matches an atomic transition, Rydberg Equation Calculator returns the wavelength of the spectral line for any upper and lower level of a hydrogen-like atom.

The photoelectric effect calculator packages the Einstein equation, NIST CODATA constants, and a built-in work function table into a single form so you can stop hand-calculating and start interpreting the numbers.

• • NIST CODATA constants baked in: Planck constant h, speed of light c, electron charge e, and electron mass m_e are from the 2019 SI redefinition, so the result matches the textbook to six significant figures.
• • Built-in work function table: Nine common metals (Na, K, Cs, Ca, Cu, Zn, W, Au, Pt) cover most modern physics problems. Switching the metal swaps phi and re-runs the Einstein equation in a single step.
• • Seven outputs from one input pair: From a wavelength and a metal you get photon energy, K_max, stopping potential, electron speed, threshold frequency, cutoff wavelength, and the work function used, all in one place.
• • No-emission guard rail: When the photon energy is below phi the calculator sets K_max = 0 and V_s = 0 and flags the case, so you do not interpret a negative K_max yourself.
• • Recalculation on every keystroke: Type a new wavelength or pick a different metal and the right-hand panel updates without reloading, which makes sweep-style homework checks almost immediate.

To see what mix of wavelengths actually reaches the metal in a real lab setup, Blackbody Radiation Calculator returns the spectral radiance curve for any temperature from a few kelvin up to stellar interiors.

Two inputs set every number on the page, and three physical constraints decide how to interpret the result.

• • The classical photoelectric approximation uses K_max = (1/2) m_e v^2 and ignores relativistic corrections. Below about 50 nm the rest energy starts to matter; the calculator flags but does not auto-correct this regime.
• • Work function values depend on the crystal face, surface contamination, and temperature. The tabulated values are clean polycrystalline room-temperature numbers; a real phototube may differ by a few tenths of an electronvolt.
• • Below the cutoff wavelength the calculator returns zero kinetic energy and zero stopping potential, which is the textbook behavior. The Einstein equation does not produce a negative K_max, and the calculator enforces that physically.

According to NIST CODATA - Sodium work function, the work function of polycrystalline sodium is 2.36 eV, the lowest of any elemental metal, and NIST CODATA - Planck constant pins Planck's constant at h = 6.62607015 x 10^-34 J*s since the 2019 SI redefinition.

The wavelength the photoelectric effect takes as input is the same lambda that appears in the wave equation, and Harmonic Wave Equation Calculator returns frequency, wave number, and angular frequency for any wavelength in any medium.