6.1992
eV
1.9392
eV
3.1070e-19
J
291
nm
1.0301e+15
Hz
1.9392
V
8.2592e+5
m/s
6.1992
eV
1.9392
eV
3.1070e-19
J
291
nm
1.0301e+15
Hz
1.9392
V
8.2592e+5
m/s
The photoelectric effect—the emission of electrons from a surface when light shines on it—was one of the key phenomena that launched the quantum revolution. While Heinrich Hertz first observed it in 1887, it was Albert Einstein's 1905 explanation using light quanta (photons) that earned him the Nobel Prize in Physics (1921). Einstein proposed that light consists of individual photons, each carrying energy E = hf, and that a single photon ejects a single electron if its energy exceeds the material's work function (φ). The Photoelectric Effect Calculator computes the maximum kinetic energy of ejected electrons, the threshold wavelength/frequency, the stopping voltage, and the maximum electron velocity. This effect is the operating principle behind photomultiplier tubes, solar cells, photodiodes, and CCD cameras, and its theoretical explanation was a cornerstone in establishing quantum mechanics.
Einstein's photoelectric equation relates the photon energy to the kinetic energy of emitted electrons:
$$KE_{\max} = h\nu - \phi = \frac{hc}{\lambda} - \phi$$
where φ is the work function (minimum energy to free an electron from the surface).
The threshold frequency (minimum frequency for emission) is:
$$\nu_0 = \frac{\phi}{h}$$
The corresponding threshold wavelength:
$$\lambda_0 = \frac{hc}{\phi} = \frac{c}{\nu_0}$$
The stopping voltage needed to halt the fastest photoelectrons:
$$eV_0 = KE_{\max} \implies V_0 = \frac{KE_{\max}}{e}$$
The maximum electron velocity:
$$v_{\max} = \sqrt{\frac{2 KE_{\max}}{m_e}}$$
Key observations: (1) Below threshold frequency, no electrons are emitted regardless of intensity. (2) KE increases linearly with frequency. (3) Electron emission is instantaneous. These cannot be explained by classical wave theory.
If the kinetic energy is zero, the photon energy exactly equals the work function—this is the threshold condition. If KE < 0 (displayed as 0), the photon lacks sufficient energy and no electrons are emitted. The stopping voltage equals the kinetic energy in eV—this is the voltage needed in a retarding-field experiment to stop all photoelectrons. Common work functions: Cs (2.1 eV), K (2.3 eV), Na (2.75 eV), Zn (3.63 eV), Cu (4.65 eV), Pt (5.65 eV). Metals with lower work functions emit electrons with lower-energy (longer wavelength) photons. The electron velocity is typically 10⁵–10⁶ m/s for UV photons on metal surfaces, small enough that relativistic corrections are unnecessary.
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200 nm UV light (6.2 eV) on zinc (φ = 3.63 eV) ejects electrons with up to 2.57 eV kinetic energy, requiring a 2.57 V stopping voltage.
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Green light barely exceeds cesium's work function, ejecting slow electrons (0.38 eV). Cesium's low work function makes it useful in photomultiplier cathodes.
The work function (φ) is the minimum energy required to remove an electron from a solid surface. It depends on the material and surface condition. Lower work function metals (Cs, K, Na) emit electrons with lower-energy photons and are used in photodetectors.
Classical theory predicts: (1) any frequency should eject electrons given enough intensity, (2) KE should depend on intensity, (3) there should be a time delay. Experiments show: (1) a threshold frequency exists, (2) KE depends on frequency not intensity, (3) emission is instantaneous. Only the photon model explains all observations.
The stopping voltage V₀ is the minimum retarding potential needed to prevent the most energetic photoelectrons from reaching the collector electrode. It equals KE_max/e in volts. Plotting V₀ vs frequency gives a straight line with slope h/e.
Einstein's 1905 paper proposed that light consists of discrete energy quanta (photons) with E = hf, explaining all features of the photoelectric effect. This was radical—even Planck considered quantization a mathematical trick. The Nobel committee awarded it in 1921 'for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect.'
Electrons are emitted with zero kinetic energy—they just barely escape the surface. This defines the threshold condition: hν₀ = φ. Any frequency below ν₀ produces no photoemission.
Intensity determines the number of photons per second, and thus the photocurrent (number of emitted electrons per second). It does not affect the maximum kinetic energy of individual electrons—that depends only on photon frequency.
Photomultiplier tubes (particle physics detectors), photodiodes (optical sensors), solar cells (photovoltaic energy), CCD/CMOS sensors (digital cameras), photoemission spectroscopy (surface analysis), and night vision devices.
The photoelectric effect ejects electrons into vacuum from a surface. The photovoltaic effect creates electron-hole pairs within a semiconductor junction, generating voltage without electrons leaving the material.
Yes. X-ray photoelectron spectroscopy (XPS) uses X-rays to eject core electrons from atoms, measuring their kinetic energy to determine binding energies and thus identify chemical elements and oxidation states.
At extremely high light intensities (lasers), an electron can absorb multiple photons simultaneously, with the effective threshold being φ/n for n photons. This nonlinear process requires intensities >10⁹ W/cm² and is used in multiphoton microscopy.
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