quantum theory

Concise Explanations of the Quantum Theory of Radiation

In 1902 Planck showed that the experimental observations in black-body radiation could be explained on the basis that the energy from the body was emitted in separate or discrete packets of energy, known as quanta of energy, of amounts hv, where v is the frequency of the radiation and h is a constant known as Planck’s constant. This is the quantum theory of radiation. With characteristic genius, Einstein asserting in 1905 that the unexpected experimental result of Lenard (that the energy of the ejected electron was independent of the intensity of the incident light and depended only on the frequency of the light) could be explained by applying a quantum theory of light. He assumed that light of frequency, V, contains packets or quanta of energy hv. On this basis, light consists of particles, and these are called photons. The number of photons per unit area of cross section of the beam of light per unit time is proportional to its intensity, but the energy of a photon is proportional to its frequency.

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The minimum amount of work or energy to take a free electron out of the surface of a metal against the attractive forces of the positive ions is known as the work function, w0, of the metal. When light of sufficiently high frequency is incident on the metal, an amount wo of the incident energy hv is used to liberate the electron, leaving an excess energy hv - wo, which is given to the ejected electron. The maximum kinetic energy, 1/2mevmax2, of the latter is thus, on Einstein’s theory:

1/2mevmax2 = hv - wo

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Milikan carried out an experiment to confirm the linear relationship between the kinetic energy of the ejected electron and the frequency expressed(1/2mevmax2 = hv - wo). Milikan carried out these experiments in 1906 using the alkali metals lithium, sodium and potassium and these metals emit electrons when illuminated by ordinary(visible) light. The negative potential V of G(gauze cylinder) relative to A(metal) when no electrons reach G is called the ‘stopping potential’ of G. here the maximum kinetic energy of the ejected electrons is just equal to the work eV done in moving against the opposing p.d. Thus:

eV=hv – w0

In trying to determine the quantum theory of radiation, Milikan found out that when the stopping potential was plotted against the frequency, a straight line PQ was obtained. Milikan used these results to calculate h and he got a value of 6.26 x 10-34 joule second, which is very close to the value of h found from experiments on black-body radiation. This confirmed Einstein’s photoelectric theory that light can be considered to consist of particles with energy hv.

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We can then write the work function energy wo as hvo, where vo=wo/h. hence, for the electrons with maximum energy,

eV = kinetic energy of electrons = hv – wo=h(v-vo)

This then means that no electrons are emitted from a metal when the incident light has frequency less than vo. The magnitude of vo is called the threshold frequency of the metal concerned.