Photoelectric Effect

**The Photoelectric Effect**

The photoelectric effect is an evidence for the particle nature of light and refers to an experiment in which electrons are emitted from the surface of a metal when being subjected to an incident light.

Photons are discrete packets of energy, when light is incident on a metal the photons which make up the light transfer their energy in a one to one ratio to the electrons of the metal. If the energy of the photon which is dependent on the frequency of the photon E=hf (h = plank's constant = 6.63x10^(-34)js) is greater or equal to the work function of the metal, then the electrons will gain enough energy to escape the metals surface. The remaining energy will be transferred into kinetic energy of the photo-electron (electron emitted from an atom after interaction with a photon). hf=ϕ+KEmax

**Experiment**

An experiment to prove the photoelectric effect can be set up using a collector and emitter plate held within vacuum with the emitter being subjected to an incident UV light. The collector is a positively charged anode and the emitter a negatively charged cathode connected by a battery in series with an ammeter. When the UV light is incident on the emitter plate photo-electrons will be emitted and attracted to the positive anode collector plate making the circuit. This will provide a current measured by the ammeter as electrons flow in the opposite direction of conventional current.

**Observations**

The photoelectric effect provides proof of a particle nature of light against a wave based model through observations which can be made of this experiment.

Threshold Frequency: When the incident light has a frequency less than this threshold no electrons will be emitted as they lack the energy required to overcome their bonds and escape the metal regardless of time the metal is subjected to the light. The threshold frequency can be calculated using hf=ϕ for a given work function. This proves a particle nature of light over a wave model as a wave model would suggest the build up of wave energy which would eventually displace the electron over time.

Instant Emission: The emission of a photo-electron is almost instantaneous when the metal is subjected to incident light and is not dependent on intensity of the light.

KE Independent of Light Intensity: Increasing the intensity of the incident light does not increase the energy transferred from the photon to electron, proving a one to one relationship of photons and electrons. Instead energy was dependent on frequency hf=ϕ+KEmax.

Rate of Emission Proportional to Intensity: When the intensity of the incident light is increased the emission of photo-electrons per second increases as there are more interactions between photons and electrons (1 to 1 ratio) providing the frequency of light is equal to or greater than the threshold for the metal and does not increase the energy transferred from or carried by the photons.

**Key Words**

Photon: Discrete packets of energy.

Photo-Electron: Electron emitted from an atom after interaction with a photon.

Threshold Frequency: Minimal frequency requirement for incident light to cause a release of electrons for a given metal.

Work Function (ϕ): Work needed to remove an electron from a given metal.

Intensity = Density of photons within light beam

**Key Equations**

E=hf (E=Energy (Joules) h = Planks Constant (Joule seconds) f= Frequency (Hertz))

hf=ϕ+KEmax (ϕ=Work Function KEmax = Kenetic Energy (Joules))

**Key Values**

Electron Volt = 1.6×10^(-19) Joules

Plank's Constant = 6.63x10^(-34)js