Photoelectric Effect Calculator
Calculate the kinetic energy of photoelectrons, threshold frequency, stopping voltage, and photon energy using Einstein's photoelectric equation: <strong>KE = hf − φ</strong>. Enter the light frequency (or wavelength) and the metal's work function to get instant results. Supports three modes: from frequency, from wavelength, and stopping voltage.
Einstein's Photoelectric Equation — KE = hf − φ
The photoelectric effect was observed experimentally in 1887 but baffled classical physicists: light below a certain frequency ejected no electrons even at high intensity, while light above that frequency immediately ejected electrons even at low intensity. Classical wave theory predicted that any frequency should work given enough intensity.
In 1905, Albert Einstein solved the puzzle by proposing that light consists of discrete packets called photons, each carrying energy E = hf (h = Planck's constant, f = frequency). A photon either has enough energy to knock out an electron or it doesn't — intensity is irrelevant to whether emission occurs. The ejected electron receives energy hf, uses φ (the work function) to escape the metal surface, and keeps the rest as kinetic energy:
KE_max = hf − φ
This equation makes three testable predictions: (1) there is a threshold frequency below which no emission occurs; (2) KE_max increases linearly with frequency; (3) intensity affects only the number of emitted electrons, not their energy. All three were confirmed by Millikan's painstaking experiments (1914–1916), and Einstein received the 1921 Nobel Prize specifically for this explanation.
How to Use the Photoelectric Effect Calculator
From Frequency mode: Enter the light frequency in hertz (e.g., 8 × 10¹⁴ Hz for near-UV) and the metal's work function in eV. The calculator computes photon energy in eV, maximum kinetic energy of the ejected electron in eV, and the threshold frequency below which no emission occurs.
From Wavelength mode: Enter wavelength in nanometers (e.g., 375 nm for near-UV) and the work function in eV. The calculator converts wavelength to frequency using f = c/λ (c = 3 × 10⁸ m/s), then applies KE = hf − φ. It also gives the threshold wavelength (the longest wavelength that can cause emission).
Stopping Voltage mode: Gives the minimum reverse voltage (in volts) needed to stop all emitted electrons. Useful for problems involving Millikan-style experiments or photodetector calibration.
Common work function values: Cs = 2.1 eV, Na = 2.3 eV, K = 2.3 eV, Zn = 4.3 eV, Cu = 4.7 eV, Pt = 5.65 eV. For UV light at 200 nm on aluminum (φ = 4.1 eV): photon energy = hc/λ = 6.2 eV, KE = 6.2 − 4.1 = 2.1 eV.
Applications of the Photoelectric Effect
Solar cells: Photovoltaic cells use semiconductor junctions rather than free electrons in vacuum, but the underlying physics is the same — photons excite electrons across a band gap. The efficiency depends on matching the photon energy distribution of sunlight to the semiconductor's band gap energy.
Photomultiplier tubes (PMTs): Used in particle physics and medical imaging (PET scanners), PMTs amplify single photons by cascading photoelectric emission through a series of dynodes. A single photon striking the photocathode releases 1–3 electrons; each dynode multiplies the count, yielding a measurable pulse from a single gamma ray.
X-ray photoelectron spectroscopy (XPS): XPS bombards a surface with X-rays and measures the kinetic energy of ejected electrons. Since KE = hf − φ and hf (X-ray energy) is known precisely, measuring KE reveals the binding energy (work function equivalent) of electrons in specific atomic orbitals — a powerful tool for surface chemistry and materials analysis.
Photodiodes and CCD sensors: Digital cameras capture images using silicon photodiodes arranged in a grid. Photons striking the silicon generate electron-hole pairs (a solid-state analog of the photoelectric effect). The charge collected in each pixel encodes light intensity, which the camera's processor converts into an image.
Frequently Asked Questions
What is the photoelectric effect equation?
Einstein's photoelectric equation is KE_max = hf − φ, where KE_max is the maximum kinetic energy of the emitted electron (in joules or eV), h = 6.626 × 10⁻³⁴ J·s (Planck's constant), f is the frequency of the incident light (Hz), and φ is the work function of the metal (the minimum energy needed to eject an electron). If hf < φ, no electrons are emitted regardless of light intensity.
What is the work function in the photoelectric effect?
The work function (φ) is the minimum energy required to eject one electron from the surface of a metal. It is a material-specific constant measured in electron volts (eV). Common values: cesium φ = 2.1 eV, sodium φ = 2.3 eV, aluminum φ = 4.1 eV, gold φ = 5.1 eV. Metals with lower work functions eject electrons with visible or near-UV light; higher work-function metals need deeper UV.
What is the threshold frequency?
The threshold frequency (f₀) is the minimum light frequency needed to eject electrons from a metal. Below f₀, no emission occurs — no matter how intense the light. It is found by setting KE = 0: f₀ = φ / h. For sodium (φ = 2.3 eV): f₀ = (2.3 × 1.602 × 10⁻¹⁹) / 6.626 × 10⁻³⁴ ≈ 5.56 × 10¹⁴ Hz (green-yellow light).
What is stopping voltage in the photoelectric effect?
Stopping voltage (V₀) is the reverse voltage needed to halt the most energetic emitted electrons. It is related to kinetic energy by eV₀ = KE_max, so V₀ = KE_max / e. If electrons are emitted with 2.5 eV of kinetic energy, the stopping voltage is 2.5 V. Millikan used stopping voltage measurements in 1916 to confirm Einstein's equation and measure Planck's constant experimentally.
Why does light intensity not affect whether electrons are emitted?
In the photon model, each electron interacts with exactly one photon. Intensity increases the number of photons hitting the surface per second, but each photon still carries energy E = hf. If that energy is below the work function, no single photon can eject an electron — adding more photons of the same frequency doesn't help. Intensity only affects the number of emitted electrons (the photocurrent), not whether emission occurs at all.
What is a real-world example of the photoelectric effect?
Solar cells, photodetectors, and digital camera sensors all exploit the photoelectric effect. In a silicon solar cell, photons with energy above silicon's band gap (~1.1 eV) excite electrons into the conduction band, generating current. Old analog darkroom photometers used cesium-coated photocells that produced current proportional to light intensity. Modern particle physics detectors (photomultiplier tubes) amplify single-photon signals via cascaded photoelectric emission.