Photoelectric effect

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to electromagnetic radiation of sufficient energy, typically in the form of light. This effect is crucial in the field of quantum mechanics and was explained by Albert Einstein in 1905, for which he received the Nobel Prize in Physics in 1921.

Key Concepts

  • Threshold Frequency ($\nu_0$): The minimum frequency of incident light required to eject electrons from the material.
  • Work Function ($\phi$): The minimum energy needed to remove an electron from the surface of the material.
  • Photoelectrons: The electrons that are emitted as a result of the photoelectric effect.
  • Stopping Potential ($V_0$): The potential difference needed to stop the fastest photoelectrons from reaching the anode in a photoelectric experiment.

Photoelectric Effect Equation

The kinetic energy (KE) of the emitted photoelectrons can be described by the equation:

$$ KE = h\nu - \phi $$

where:

  • $KE$ is the kinetic energy of the photoelectron,
  • $h$ is Planck's constant ($6.626 \times 10^{-34} \text{ J}\cdot\text{s}$),
  • $\nu$ is the frequency of the incident light,
  • $\phi$ is the work function of the material.

If the kinetic energy is expressed in terms of the stopping potential, the equation becomes:

$$ eV_0 = h\nu - \phi $$

where:

  • $e$ is the elementary charge ($1.602 \times 10^{-19} \text{ C}$),
  • $V_0$ is the stopping potential.

Experimental Setup

The typical experimental setup for observing the photoelectric effect includes:

  • A light source that emits photons of varying frequencies.
  • A metal surface (cathode) that will emit electrons when struck by photons.
  • An anode to collect the emitted electrons.
  • A variable stopping potential to determine the kinetic energy of the emitted electrons.

Observations and Conclusions

  1. Emission of Electrons: Electrons are emitted from the metal surface as soon as the light with a frequency higher than the threshold frequency shines on it.
  2. Energy of Electrons: The maximum kinetic energy of the emitted electrons is independent of the intensity of the light but depends on its frequency.
  3. Threshold Frequency: No electrons are emitted if the frequency of the incident light is below the threshold frequency, regardless of the intensity.
  4. Intensity of Light: The number of electrons emitted per unit time (photoelectric current) is proportional to the intensity of the incident light, provided the frequency is above the threshold.

Differences and Important Points

Aspect Photoelectric Effect
Nature of Light Light behaves as a particle (photon) with energy $E = h\nu$.
Threshold Frequency Below $\nu_0$, no electrons are emitted, regardless of light intensity.
Kinetic Energy $KE$ of photoelectrons increases linearly with the frequency of the incident light.
Intensity of Light Increasing the intensity increases the number of emitted electrons, not their energy.
Instantaneous Response Electron emission is instantaneous with the absorption of photons above $\nu_0$.
Work Function Material-specific constant, $\phi$, related to the minimum energy needed to emit electrons.

Examples

Example 1: Calculating Kinetic Energy

Suppose a light of frequency $\nu = 1.5 \times 10^{15} \text{ Hz}$ shines on a metal with a work function $\phi = 2.0 \text{ eV}$. The kinetic energy of the emitted photoelectrons can be calculated as follows:

First, convert the work function to joules:

$$ \phi = 2.0 \text{ eV} \times 1.602 \times 10^{-19} \text{ J/eV} = 3.204 \times 10^{-19} \text{ J} $$

Now, use the photoelectric equation:

$$ KE = h\nu - \phi $$ $$ KE = (6.626 \times 10^{-34} \text{ J}\cdot\text{s})(1.5 \times 10^{15} \text{ Hz}) - 3.204 \times 10^{-19} \text{ J} $$ $$ KE = 9.939 \times 10^{-19} \text{ J} - 3.204 \times 10^{-19} \text{ J} $$ $$ KE = 6.735 \times 10^{-19} \text{ J} $$

Example 2: Stopping Potential

If the stopping potential required to halt the fastest photoelectrons in the previous example is to be found, use the equation:

$$ eV_0 = KE $$ $$ V_0 = \frac{KE}{e} $$ $$ V_0 = \frac{6.735 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ C}} $$ $$ V_0 \approx 4.21 \text{ V} $$

The stopping potential is approximately 4.21 volts.

Conclusion

The photoelectric effect demonstrates the particle nature of light and is a cornerstone of quantum mechanics. It shows that light can be thought of as consisting of particles called photons, each carrying a quantum of energy. The effect has numerous applications, including in photovoltaic cells, photoelectron spectroscopy, and light detection technologies.