Question

Explain, briefly one of the phenomena below and describe how it relates to quantization of energy. (a) the photoelectric effect OR (b) line (emission) spectra

Answer 1

The photoelectric effect is a phenomenon in which electrons are ejected from the clean surface of certain metals (alkali metals), when the metals are exposed to a light. For the emission of electrons from the metal, light of a minimum frequency, called the threshold frequency only will be effective. The number of electrons ejected was proportional to the intensity (or brightness) of the light. But the energies of the ejected electrons do not depend on the intensity of the radiation. They depend on the frequency of the incident radiation. If ν is below the threshold frequency no electrons will be ejected, no matter how great the intense the light.

Figure below is an apparatus for studying the photoelectric effect. The flow of electrons is registered by a detecting meter. Certain cameras work on the basis of photoelectric effect.

It is observed that violet light is able to eject electrons from potassium but red light has lower frequency has no effect. The explanation for the frequency dependence of the photoelectric effect is given by Albert Einstein. Einstein argued that the wave model of light cannot explain the observed facts. Planck’s photoelectric effect fails to explain the wave theory of light. Using Planck’s quantum theory of radiation as a starting point, Einstein explained the photoelectric effect. He deduced that each photon must possess energy E, given by the equation

                                                        E=hν

Where, ν is the frequency of light. Einstein received the Nobel Prize in physics in 1921 for his explanation of the photoelectric effect.

Shining a beam of light on to a metal surface can, therefore, be viewed as shooting a beam of particles, the photons. When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy instantaneously to the electron during the collision and the electron is ejected without any time lag or delay. Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron. In other words, kinetic energy of the ejected electron is proportional to the frequency of the electromagnetic radiation. Since the striking photon has energy equal to hν and the minimum energy(binding energy BE) required to eject the electron is hν₀ (also called work function,W), then the difference in energy (hν – hν₀ ) is transferred as the kinetic energy of the photoelectron.

i.e., KE = (hν – hν₀ )

This shows that the more energetic the photon (that is, the higher its frequency), is greater will be the kinetic energy of the ejected electron.

Now consider two beams of light having the same frequency (which is greater than the threshold frequency) but different intensities. The more intense the beam of light consists of a larger number of photons; consequently, it ejects more electrons from the metal’s surface than the weaker beam of light. Thus, the more intense the light is, the greater would be the number of electrons emitted by the target metal; similarly higher the frequency of the light is, the greater would be the kinetic energy of the ejected electrons.