Analyse the photoelectric effect ?max=ℎ?−? as it occurs in metallic elements by applying the law of conservation of energy and the photon model of light
Experimental evidence suggested the following :
- For a given metal surface, there exists a certain minimum frequency of incident radiation below which no photoelectrons are emitted. This frequency is called the threshold frequency.
- Increasing the frequency of the incident beam, keeping the intensity constant increases the maximum kinetic energy of the photoelectrons emitted.
- Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident light, but is independent of the intensity of the incident light (so long as the latter is not too high)
In 1905, Albert Einstein successfully explained the photoelectric effect by adding to the quantum theory created by Planck.
- He proposed that electromagnetic waves exists as photons.
- If a photon strikes a metal surface, it will collide with a single electron in an atom in the metal and transfer all of its energy to the electron.
- A certain minimum energy is required to cause the emission of an electron from the metal surface (known as work function of that metal).
- Each photon has energy equivalent to . (being frequency of the EM wave)
- If the photon contains more energy than the work function , then the rest of the energy is transferred as Kinetic energy of the electron.
- Light intensity is dependant on the number of photons.
- Increasing the intensity of the light increases the rate at which photons fall on the metal surface hence the rate of emission of photoelectrons increases.
With this theory and further experimental evidence, it was observed that ;
- If we plot the kinetic energies of the electrons with max kinetic energies emitted from a metal surface due light, against the frequency of the incident light, then we get a straight line with the same slope for all metals.
- This mathematically corresponds to :
- where : is work function or minimum energy required
- f is frequency of the incident light
- h is known as planck’s constant
- Kmax is the kinetic energy of the escaped electron with the maximum kinetic energy.