Calculator Inputs
Formula Used
How to Use This Calculator
- Pick a method that matches your measurements.
- Enter the required values and select correct units.
- Click Calculate to view results above the form.
- Use CSV or PDF buttons to export the latest result.
- If the work function is negative, recheck units.
Example Data Table
| Material | Wavelength (nm) | Stopping Potential (V) | Photon Energy (eV) | Work Function (eV) |
|---|---|---|---|---|
| Sodium (example) | 400 | 0.60 | 3.10 | 2.50 |
| Potassium (example) | 500 | 0.20 | 2.48 | 2.28 |
| Copper (example) | 250 | 1.60 | 4.96 | 3.36 |
| Zinc (example) | 220 | 1.30 | 5.64 | 4.34 |
| Aluminum (example) | 200 | 1.00 | 6.20 | 5.20 |
Work Function Insights and Measurement Notes
1) What the work function represents
The work function (φ) is the minimum energy needed to move an electron from a solid into vacuum. Because it depends on the surface, thin oxide layers, adsorbed gases, and polishing can shift φ by noticeable amounts.
2) Typical ranges you will encounter
Many alkali metals have relatively low φ values (often ~2–3 eV), enabling photoemission with visible light. Common metals used in engineering are higher: aluminum is frequently around ~4 eV, copper near ~4.5–5 eV, and gold often around ~5 eV.
3) Converting wavelength to photon energy
Photon energy can be computed from wavelength using E = hc/λ, so shorter wavelength means higher energy. A practical approximation is E(eV) ≈ 1240/λ(nm). For example, 400 nm light is about 3.10 eV, while 250 nm ultraviolet is about 4.96 eV, commonly exceeding the work function of many metals.
4) Frequency method and linear trends
If you measure at several frequencies, the photoelectric relation Kmax = hf − φ predicts a straight line when plotting Kmax versus f. The slope is Planck’s constant h, and the intercept gives −φ.
5) Using stopping potential to obtain Kmax
In many setups you measure a stopping potential Vs, which relates to maximum kinetic energy by Kmax = eVs. A stopping potential of 0.60 V corresponds to 0.60 eV. The calculator subtracts this Kmax from the photon energy to estimate φ consistently.
6) Threshold frequency and wavelength checks
At the threshold, electrons are emitted with nearly zero kinetic energy, so φ = hf0. The reported f0 and λ0 help you verify feasibility: if your source wavelength is longer than λ0, photoemission should be weak or absent for that surface.
7) Common sources of uncertainty
Negative φ results usually indicate a unit mismatch (nm vs µm), an overstated stopping potential, or inconsistent energy units. In experiments, contact potentials, space‑charge, lamp bandwidth, and stray light can distort the cutoff. Taking repeated runs and averaging Vs values improves stability.
8) Where the calculated value is used
Work function supports decisions in photocathodes, electron optics, vacuum electronics, and surface science. In semiconductors and metal contacts, φ influences barrier heights and charge transfer at interfaces. In emission models, small changes in φ can strongly affect current density, so tracking φ helps diagnose surface processing and aging.
FAQs
1) What is a typical work function value?
Many clean metals fall between about 2 and 5.5 eV. Alkali metals are often lower, while noble and transition metals are higher. Surface oxidation and contamination can change the value substantially.
2) Why did I get a negative work function?
Usually the photon energy was entered too small or the kinetic energy too large due to unit mistakes. Recheck wavelength units, frequency multipliers, and whether kinetic energy is in eV or joules.
3) Is stopping potential equal to kinetic energy?
Stopping potential is a voltage. The maximum kinetic energy equals eVs, which becomes numerically the same in eV units. For example, 0.8 V corresponds to 0.8 eV.
4) Which method should I choose?
Pick the method that matches what you measured. If you have a cutoff voltage, use a stopping‑potential method. If you measured a threshold wavelength or frequency, use the threshold options for direct φ.
5) What does threshold wavelength mean?
Threshold wavelength λ0 is the longest wavelength that can still eject electrons. Light with wavelength longer than λ0 generally lacks enough photon energy to overcome the surface barrier.
6) Should I use more significant figures?
Use significant figures that match your measurement precision. If wavelength is known to only three digits, reporting ten digits for φ is misleading. For most lab work, 4–6 significant figures is sufficient.
7) Do temperature and surface condition matter?
Yes. Heating can change adsorption and surface states, and oxides can increase the effective barrier. Cleaning, vacuum quality, and time since preparation often change measured φ more than instrument rounding.