Photoelectric Effect Calculator

How to use the Photoelectric Effect Calculator

What this calculator does

This calculator applies Einstein's photoelectric equation to a single incident photon and a material threshold. It converts the light description into frequency, wavelength, and photon energy; converts the material threshold into both threshold frequency and work function; and then determines the maximum kinetic energy available to an emitted electron. It also reports the equivalent stopping potential. The model is an idealized energy-balance calculation: it tells you whether the photon has enough energy to overcome the work function and, if so, how much maximum kinetic energy remains. It does not predict photocurrent, quantum efficiency, surface contamination, electron scattering, or the number of electrons emitted.

The governing relationships are the standard ones described in the OpenStax treatment of the photoelectric effect: photon energy is E = hf, the work function is φ = hf₀, and the maximum kinetic energy above threshold is K_max = hf – φ. The stopping potential satisfies eV_s = K_max.

When to use it

• Check whether a laser or monochromatic source can eject electrons from a material with a known threshold frequency or work function.
• Convert between frequency, wavelength, and photon energy while keeping the same physical incident-light state.
• Estimate maximum photoelectron kinetic energy and stopping potential for a classroom experiment or lab-planning calculation.
• Explore how changing photon frequency or material work function changes the threshold for photoemission.

How to calculate

1. The calculator opens with a complete demonstration: an incident frequency of 700 THz and a threshold frequency of 600 THz. Results are already calculated, and Download Excel is immediately available for this example.
2. Use Incident light representation to choose Frequency (THz), Wavelength (nm), or Photon energy (eV). When you change this representation, the current incident value is converted rather than reinterpreted.
3. Enter the corresponding positive number in Incident light value. Use a decimal point for decimals. Commas are accepted only as standard three-digit thousands separators, so an ambiguous value such as 1,5 is rejected rather than silently turned into 15.
4. Use Material threshold representation to choose Threshold frequency (THz) or Work function (eV), then enter its positive value in Material threshold value. Switching representation converts the same material threshold.
5. Read Maximum kinetic energy first, then use Stopping potential, Photon energy, Work function, wavelength outputs, and the calculation table for context. The summary pills show the emission state, photon energy, and threshold frequency.
6. Select Download Excel to create a workbook from the current validated state. Reset clears the demonstration and all calculated content; after Reset, Excel export is disabled until a new complete valid pair is entered.

Input guide

Incident light representation is required and selects the physical form of the incoming photon. Frequency (THz) expects terahertz, Wavelength (nm) expects nanometres, and Photon energy (eV) expects electronvolts. For example, 700 THz describes visible violet-blue light. Higher frequency means higher photon energy; longer wavelength means lower photon energy. A common mistake is changing the representation and then manually copying the old number into the new unit – the calculator already performs the conversion for you.

Incident light value is a required positive decimal. In the startup example it is 700 THz. The accepted format uses a period as the decimal separator, with optional correctly grouped commas such as 1,000. Scientific notation such as 7e2 is intentionally rejected in the form so pasted values cannot be misread. Increasing frequency or photon energy increases the available energy; increasing wavelength decreases it.

Material threshold representation is required. Threshold frequency (THz) is the minimum photon frequency associated with the material's work function, while Work function (eV) is the corresponding minimum energy. The startup example uses Threshold frequency. Switching to Work function converts the same threshold, so the physical result should remain unchanged apart from display rounding.

Material threshold value is a required positive decimal. The demonstration uses 600 THz, equivalent to about 2.4814 eV. A higher threshold frequency or work function makes photoemission harder, reducing the energy surplus for a fixed light source. Real material work functions depend on surface condition, crystal face, and contamination, so use a value appropriate to the surface being studied rather than assuming one universal number.

Output guide

State reports Emitting, At threshold, or Below threshold. Emitting means the incident photon frequency is above the material threshold. At threshold means the idealized energy surplus is effectively zero. Below threshold means the photon does not have enough energy to overcome the work function. This status is an ideal threshold result, not a prediction of current magnitude.

Maximum kinetic energy is the primary result in electronvolts. It is zero at or below the threshold and positive above it. Stopping potential is the voltage whose electron-charge energy equals that maximum kinetic energy; numerically, a kinetic energy of 0.413567 eV corresponds to 0.413567 V for one electron. Photon energy is hf. Work function is hf₀. Incident wavelength and Threshold wavelength use c = fλ. Energy surplus / deficit preserves the signed difference E – φ: positive values are available kinetic energy, zero is threshold, and negative values show how far the photon falls short.

The Calculation details table repeats the canonical frequency, wavelength, photon energy, threshold frequency, work function, energy balance, maximum kinetic energy, and stopping potential with symbols and interpretations. It is most useful when checking unit conversions or documenting a calculation, and its numeric source is the same model used by the Excel workbook.

Worked example

With the startup inputs f = 700 THz and f₀ = 600 THz, the frequency difference is 100 THz = 1.00 × 10¹⁴ Hz. Using the exact SI Planck constant h = 6.62607015 × 10 ^{– 34} J·s, the kinetic-energy surplus is h(f – f₀) = 6.62607015 × 10 ^{– 20} J. Dividing by the exact elementary charge gives 0.4135667697 eV, displayed as 0.413567 eV. The photon energy is 2.894967 eV, the work function is 2.481401 eV, and the stopping potential is 0.413567 V. The NIST SI constants reference documents the exact values of h, e, and c used here.

Learn more

The photoelectric effect was central to the development of quantum physics because electron kinetic energy depends on photon frequency rather than simply on light intensity. For another concise university explanation of the threshold-frequency idea and work function, see Boston University's notes on photons and the photoelectric effect.