Work Function from Stopping Potential Calculator

Examples are illustrative; real measurements depend on surface condition and calibration.

The photoelectric equation relates photon energy to the stopping potential: eV_s = hf − φ. Solving for the work function gives: φ = hf − eV_s.

• h is Planck’s constant.
• e is the elementary charge.
• f = c/λ when wavelength is provided.
• Cutoff frequency: f₀ = φ/h, cutoff wavelength: λ₀ = c/f₀ (when φ > 0).

Practical note: If φ becomes negative, the chosen light energy is insufficient for the requested stopping voltage, or the inputs describe a nonphysical combination.

1. Select an input mode: frequency, wavelength, or photon energy.
2. Enter the measured stopping potential and choose its unit.
3. Provide the light description in the chosen mode and unit.
4. Press Calculate to view results above the form.
5. Use Download CSV or Download PDF to save outputs.

For best results, use consistent experimental conditions, clean emitter surfaces, and calibrated voltmeters. Consider adding uncertainties to estimate confidence in φ.

1) What this calculator delivers

This tool estimates a material’s work function (φ) by combining measured stopping potential with a chosen description of incident light. Output is provided in joules and electronvolts, alongside the implied wavelength and frequency for consistency checks. A clear summary helps you compare materials and document experiments.

2) Photoelectric model behind the numbers

In the photoelectric effect, photons transfer energy to electrons. The stopping potential is the retarding voltage that reduces the photocurrent to zero, revealing the maximum kinetic energy of emitted electrons. With reliable inputs, φ captures the minimum energy barrier an electron must overcome to escape the surface.

3) Choosing your input data source

Laboratories report light as frequency (Hz), wavelength (m), or photon energy (eV). The calculator accepts all three. For optical setups, wavelength is often measured directly; for RF or laser systems, frequency is convenient; and for spectroscopy, energy in eV or keV may be the native quantity.

4) Unit conversions that matter

Internally, values are converted to SI to prevent scaling mistakes. Frequency units span Hz to PHz, wavelength units include Å to meters, and stopping potential supports mV to kV. Because 1 eV equals the energy gained by one electron across 1 volt, the maximum kinetic energy in eV numerically equals the stopping potential in volts.

5) Reading the work function result

The reported φ is computed as photon energy minus the electron’s maximum kinetic energy. If φ is positive, the inputs are physically consistent for emission. If φ becomes negative, either the stopping potential is too large for the supplied photon energy, or the measurement conditions are inconsistent with the ideal model.

6) Typical ranges for real materials

Work functions depend on surface condition, crystallographic orientation, and contamination. As a practical reference, alkali metals often fall near 2–3 eV, common conductors such as aluminum and copper are frequently around 4–5 eV, and noble metals can be closer to 5–6 eV. Use these ranges to sanity‑check outputs before publishing results.

7) Uncertainty, precision, and repeatability

Small voltage errors can shift φ measurably. If you provide uncertainties for stopping potential and frequency, the tool estimates uncertainty in φ using standard propagation. Improve repeatability by stabilizing light intensity, minimizing stray fields, cleaning the cathode surface, and averaging repeated stopping-voltage measurements.

8) Practical uses and reporting

Work function estimation supports material identification, surface treatment validation, and detector/photocathode characterization. In reports, record light parameters, stopping potential, temperature, and vacuum level. Export the CSV for lab notebooks and generate a PDF summary for quick peer review or coursework submission.

1) What is “stopping potential” in this context?
It is the reverse (retarding) voltage that reduces photocurrent to zero, indicating the maximum kinetic energy of emitted photoelectrons.

2) Why does kinetic energy in eV equal the stopping potential in volts?
One electron accelerated through 1 volt gains 1 electronvolt of energy, so K_max(eV) = V_s(V) for single‑electron charge.

3) Which input mode should I use: frequency, wavelength, or energy?
Use the quantity you measure most directly. Wavelength suits optics, frequency suits RF/lasers, and photon energy suits spectroscopy and X‑ray sources.

4) What does a negative work function result mean?
It usually indicates inconsistent inputs: the stated stopping potential is too large for the photon energy, or the experiment deviates from the idealized photoelectric model.

5) Does surface contamination affect work function?
Yes. Oxides, adsorbates, and roughness can shift the effective work function significantly, so clean surfaces and controlled environments improve accuracy.

6) What are cutoff frequency and cutoff wavelength?
They are threshold values where emission just begins: f₀ = φ/h and λ₀ = c/f₀, shown only when φ is positive.

7) How should I document results for a lab report?
Record the light parameter, stopping potential, units, instrument resolution, and conditions. Export CSV for tables and PDF for a clear summary section.