Monochromatic light of frequency 6 . 0 × 10 14 Hertz is produced by a laser. What is the energy of a photon in the light beam? h = 6 . 63 × 10 - 34 JS

Each photon has an energy , E = h . v = 6 . 63 × 10 34 J s 6 . 0 × 10 14 Hz = 3 . 98 × 10 - 19 J

What is thermionic emission?

Thermionic emission is the emission of electrons from a heated metal (cathode). This principle was first used in the Coolidge tube and then later in the modern day x-rays tube. Before the discovery of the principle, gas tubes were used for x-rays production. The cathode has its filament circuit that supplies it with necessary filament circuit to heat it up. As the temperature increases, the surface electrons gain energy. The energy acquired by the surface electrons allows them to move a short distance off the surface thus resulting in emission. A pure tungsten filament must be heated to a temperature of 2200 degree celcius To emit a useful number of electrons. The electrons emitted from the surface are limited by the space charge effect.

The work function of a metal is 0 . 1 eV . Calculate the threshold frequency for photoelectric emission.

The first theory of the photoelectric effect was put forward by Einstein by using Max Planck’s theory of light energy being quantized. It was considered that each packet of light energy or photons carried energy hv where h was a proportionality constant known as the Planck constant and v was the frequency of the electromagnetic waves of light. Kmax is the maximum amount of kinetic energy delivered to the atoms before they leave their atomic bonding ϕ 0 = 0 . 1 eV = 0 . 1 × 1 . 6 × 10 - 19 J h = 6 . 6 × 10 - 34 J - sec ϕ 0 = hv 0 v 0 = ϕ 0 h = 0 . 1 × 1 . 6 × 10 - 19 6 . 6 × 10 - 34 v 0 = 0 . 029 × 10 15 Hz

Establish Einstein's relation 1 2 mu 2 = hv - hv 0 with respect to photoelectric emission.

The phenomenon of emission of electrons from a metal surface, when electromagnetic radiations of sufficiently high frequency are incident on it, is called the photoelectric effect. Einstein explained the photoelectric effect based on Planck's quantum theory according to which light radiation travels in the form of discrete photons. The energy of each photon is hv , where h is Planck's constant and v is the frequency of light. The main points of Einstein’s theory of the photoelectric effect are: The interaction between two particles results in photoelectric emission– one a photon of incident radiation and the other an electron of photosensitive metal. The free electrons are bound within the metal due to restraining forces on the surface. The minimum energy required to liberate an electron from the metal surface is called the work function W 0 of the metal. Each photon interacts with one electron. The energy hv of the incident photon is used up in two parts: A part of the energy of the photon is used in liberating the electron from the metal surface, which is equal to the work function W 0 of the metal, and The remaining energy of the photon is used in impairing kinetic energy to the ejected electron. Very few < 1 0 0 photons, whose energies are greater than W 0 , capable of ejecting the photons. By law of the conservation of energy, Energy of the incident photon = Maximum K . E . of photon + Work function hv = 1 2 mv 2 max + W 0 ∴ K max = 1 2 mv 2 max = hv - W 0 . . . . . . . ( 1 ) If the incident photon is threshold frequency v 0 , then its energy hv 0 is just sufficient to free the electron from the metal surface and does not give it any kinetic energy. So hv 0 = W 0 . Hence K max = 1 2 mv 2 max = hv - hv 0 = h v - v 0 . . . . . . ( 2 ) Equations (1) and (2) are called Einstein’s photoelectric equations.A