Photoelectric effect calculator

The same pure arithmetic runs free in the browser and at $0.002 per successful API call, with no network, sampling, or date-dependent shortcuts. A photon frequency that is missing, zero, negative, or non-finite fails with invalid_input and is not billed.

What Einstein's photoelectric equation means and what the response contains

This calculator returns that maximum kinetic energy in joules, the photon energy h f, the work function you supplied, the threshold frequency phi over h, electronvolt companions of those energies, and a boolean ejected that is true when h f is at least phi. Below threshold the leftover would be negative, which cannot be a kinetic energy of an ejected electron, so max_kinetic_energy is reported as zero and ejected is false. There is no table of named metals and no wavelength-to-frequency conversion inside this endpoint: you supply frequency in hertz and work function in joules, and the engine either evaluates the Einstein remainder or rejects a non-positive frequency with invalid_input.

Input contract, units, and how K_max stays reproducible

Convert a textbook value in electronvolts by multiplying by the elementary charge 1.602176634 times ten to the minus nineteen coulombs, so 2.3 eV becomes about 3.685 times ten to the minus nineteen joules. Convert terahertz to hertz by multiplying by ten to the twelve, so 500 THz becomes 5 times 10 to the 14 hertz. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected so a bad cell does not become a wrong kinetic energy. Magnitudes above the documented ceilings for frequency and work function are rejected so overflow cannot silently become Infinity. Computation multiplies the exact SI 2019 Planck constant by frequency, subtracts the work function, and clamps a negative leftover to zero so the published maximum kinetic energy is never a non-physical negative joule value. Failed validation is not billed. POST a JSON body with two required finite numbers. Frequency is the incident photon frequency f in hertz; aliases f, nu, and frequency_hz are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. It must be strictly positive: zero, negative, negative zero, NaN, and Infinity fail with invalid_input naming frequency, because the photoelectric equation K_max equals h f minus phi is undefined for a non-positive frequency. Work function is the metal work function phi in joules; aliases phi, work_function_j, and phi_j are accepted. It must be a finite non-negative number. On success the body echoes frequency and work_function, reports photon_energy and photon_energy_ev, work_function_ev, threshold_frequency, max_kinetic_energy and max_kinetic_energy_ev, ejected, the exact constants h and elementary_charge, a unit string J, the method tag photoelectric_effect, and a short formula reminder.

Where a photoelectric-effect calculator earns its keep

Laboratory courses that measure stopping potential versus frequency still need a closed-form Einstein remainder to compare against a fitted slope h and intercept phi; calling a tiny parse API avoids pulling a computer-algebra system for two scalars. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split of free interactive exploration and a priced, identical API matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.