3.2 Sspd chapter 1_part 2_photoelectric effect

1.2. PHOTO-ELECTRIC EFFECT AND EINSTEIN EQUATION.

V _R = Retarding Voltage;

K = Cathode;

A= Anode;

W _F = Work-Function of the Cathode which is Thoriated Tunsten coated with Strontium Barium Oxide;

Photon Energy minus the Work-Function gives the kinetic energy of the photo-emitted electrons coming out of the cathode in the vacuum space surrounding the cathode;

hν – W _F = (1/2)m _e v ² = qV _R ; This Equation implies that if there is retarding voltage on the Anode then photo-emitted electron with a kinetic energy (1/2)m _e v ² is totally expended in climbing up the Potential Hill created by the Retarding Voltage. Hence no photo current is detected by the Anode.

Fig.1.2. The Apparatus for verifying Photo Electric Effect and Einstein Equation.

Figure.1.2. describes the Experimental Set Up for verifying Photo Electric Effect and Einstein Equation. It consists of a Vacuum Tube which consists of a Cathode and an Anode. A Vacuum Tube is evacuated to an air pressure of 10 ^-3 mm of Mercury which is referred to as 10 ^-3 Torr. [ 1 Torr is the pressure which supports 1 mm of column of mercury. Torr is in the honour of the scientist Torrceli. Torrceli was the scientist who suggested that there was a near vacuum above the 76cm column of mercury supported by atmospheric pressure. When a 85cm tall glass tube , filled with mercury, is inverted over a trough full of mercury then only 76cm column is supported. The space above this column within the tube is empty except for mercury vapour which is negligible because of very high cohesive force between the molecules of Mercury. This empty space is referred to as Torcelli vacuum.]

An accelerating voltage or decelerating voltage can be applied to the Anode A Monochromatic beam of light of frequency ν is obliquely incident through a side tube on the Cathode for photo-ionic emission of electrons from the Cathode.

The Energy Band Diagram, which will be derived in Section 1.8., is given in Fig.1.3. As seen from the Diagram, the outermost unfilled Band is known as Conduction Band. At Zero Kelvin ,the Conduction Band is completely occupied till Fermi Energy Level E _F . As the temperature is raised , by Equipartition Law of Energy the Conduction Band electrons have (1/2)kT Average Thermal Energy associated with each degree of freedom and semi-free electrons in Conduction Band have three translational degree of freedoms. Hence the average thermal energy associated with the semi-free electrons in Conduction Band is (3/2)kT Joules. How the electrons are distributed above and below the Fermi-Level Energy at temperature T Kelvin will be clear when we discuss Fermi-Dirac Statistics.

E F = Fermi level Energy. It lies within the band gap for metal.

E G = Energy Band Gap = Forbidden Zone.

E C = Lower Edge of the Conduction Band.

E V = Upper Edge of the Valence Band.