The photoelectric effect

• When photons of electronmagnetic radiation are incident on a metal surface they may liberate electrons
• Photons carry energy and this is linked to their frequency and wavelength:
• E(photon) = hf = (hc)/λ
• The higher the frequency, the more energy that the photon is carrying hence the electron that is displaced has a greater kinetic energy

• When normal light is incident on a negatively charged plate nothing happens
• When UV light is incident on a negatively charged plate it discharges instantly; there is no decay
• No matter how strong normal visible light is, the plate is not discharged
• The rate of emission of electrons is proportional to the intensity of the light so long as it is above a certain threshold frequency

• Ultraviolet Radiation from a UV lamp is directed at the surface of a zinc plate placed on the cap of a gold leaf electroscope. This device is a very sensitive detector of charge. When it is charged, the thin gold leaf of the electroscope rises- it is repelled from the metal stem, as they both have the same type of charge.
• If the electroscope is charged negatively  the leaf rises and stays in position. However if UV light is directed at the zinc plate, the leaf gradually falls as conduction electrons at the zinc surface leave it when UV light is directed at it. The emitted electrons are referred to as photoelectrons.
• If the electroscope is charged positively, the leaf rises and stays in position, regardless of whether or not UV light is directed at the zinc plate.

If you consider photons to be particulate in nature when they collide with the metal then you can say:

• One photons hits one electron and gives all of its energy to that single electron
• The energy will leave the metal surface only if the energy it is given is above a certain value called the work function which is specific to the metal used
• If the electron does not leave then it loses the energy to surrounding electrons rapidly (which slowlt heats the metal)

Ek(max) = hf - Φ (Φ = work function)

• The energy from the photon is given to the electron in the metal. Some of this is then used to escape the metal and the remainder is the kinetic energy of the photoelectron
• The electron can have less energy than the calculated amount if it was buried just under the surface if the metal (so needed more to leave)

Emission takes place if:

• Ek > 0
• hf > Φ 

• You can equate the formula and make the kinetic energy zero (i.e. the electron can only just leave the surface of the metal) and rearrange to give the following formula:
• f(min) = Φ/h