Cathode Rays

Cathode rays are the stream of fast moving electrons. These rays are produced in a discharge tube at a pressure below 0.01 rom of mercury.

Properties of Cathode Rays

• Cathode rays are not electromagnetic rays.
• Cathode rays are deflected by electric field and magnetic field.
• Cathode rays produce heat in metals when they fall on them.

Specific charge of cathode rays means ratio of charge and mass. Specific charge of electron was determined by J J Thomson .Specific charge of electron  = (e / m)  . The value of specific charge of an electron is 1.7589 * 10¹¹ C / kg.

Millikan measured the charge of an electron through his popular oil drop experiment.

The charge of the electron as determined by Millikan was found to be 1.602 * 10^-19 C.

Electron Emission

It is the phenomenon of emission of electron from the surface of a metal. Electron emission can obtained from the following process

• Thermionic – By suitable heating, provide sufficient thermal energy.
• Photoelectric emission - When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface. These photo(light)-generated electrons are called photoelectrons.
• Field emission - By applying a very strong electric field to a metal.

Photoelectric Effect

The phenomena of emission of electrons from a metal surface, when radiations of suitable frequency is incident on it, is called photoelectric effect.

Terms Related to Photoelectric Effect –

• Work Function( φ0) The minimum amount of energy required to eject one electron from a metal surface, is called its work function.
• Threshold Frequency (ʋ_o) The minimum frequency of light which can eject photo electron from a metal surface is called threshold frequency of that metal.
• Threshold Wavelength (λ_max) The maximum wavelength of light which can eject photo electron from a metal surface is called threshold wavelength of that metal.
• Relation between work function, threshold frequency and threshold wavelength

φ0 = hʋ_o = (hc / λmax )

Laws of Photoelectric Effect - (Basic features)

1. For a given metal and frequency of incident light, the photo electric current ( rate of emission of photoelectrons) is directly proportional to the intensity of incident light. Means number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
2. For a given metal, there is a certain minimum frequency, called threshold frequency, below which there is no emission of photoelectrons takes place.
3. For above threshold frequency, the maximum kinetic energy of photoelectrons depends upon the frequency of incident light.
4. The photoelectric emission is an instantaneous process.

Effect of potential on photoelectric current-

• Saturation current- Maximum value of the photoelectric current is called saturation current.
• Stopping Potential (Vo). The minimum negative potential at which photoelectric current becomes zero.
• Maximum kinetic energy of photo electrons

 (K.E.)max = ( ½) mv²_max = e.Vo

• For a given frequency of the incident radiation, thestopping potential is independent of its intensity. Means maximum kinetic energy of photoelectrons depends on the light sourceand the emitter plate material, but is independent of intensity of incident

Effect of frequency of incident radiation on stopping potential –

• greater thefrequency of incident light, greater is themaximum kinetic energy of the photoelectrons.
• there exists certain minimum cut-off (threshold) frequency ν0 for which stopping potential is zero.
• maximum kinetic energy of the photoelectrons and stopping potential V0  varies linearlywith the frequency of incident radiation, but is independent of its
• frequency ν of incident radiation, lower than threshold frequency (ν0 ) , no photoelectric emission is possible even if theintensity is large.

For a given photosensitive material & frequency ( ʋ > ʋ_o ) of incident radiation - photoelectric current is directly proportional to intensity of incident light. Stopping potential or equivalent maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of its intensity.

PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT—

Phenomena of interference, diffraction and polarization explained in a natural and satisfactory way by the wave picture of light— light is an electromagnetic wave consisting of electric and magnetic fields with continuous distribution of energy over the region of space over which the wave is extended.

Wave theory is unable to explain the most basic features of photoelectric emission ?

• According to the wave theory of light, the free electrons at the surfaceof the metal absorb the radiantenergy continuously, when beam of radiation falls on it. So greater the intensity of radiation, the greater arethe amplitude of electric and magnetic fields.Greaterthe intensity, the greater should be the energy absorbed by each electron.maximum kinetic energy of the photoelectrons is then expected to increase with increase in intensity. So it’s not depend on frequency of radiation. So threshold frequency does not exist in wave theory. So it contradict with basic feature of photoelectric emission.
• Photoelectric emission is instantaneous process. But in the wave picture, the absorption ofenergy by electron takes place continuously over the entirewavefront of the radiation.Energy absorbed per electron per unit time turns out to be small. So it take much time to absorb sufficient energy to come from surface, so it contradict that photoelectric process is instantaneous process.

EINSTEIN’S PHOTOELECTRIC EQUATION : ENERGY QUANTUM OF RADIATION—

• Einstein proposed a radically new theory of electromagnetic radiation to explain photoelectric effect. Radiation energy is buildup of discrete units called quanta of energy of radiation.Each quantum of radiant energy has energy = hʋ, where h is Planck’s constant and ʋ is thefrequency of light.
• If radiation absorbed by photoelectron having quantum of radiation energy hʋ exceeding the work function then then photoelectron come out with maximum kinetic energy
• (K)­_MAX = hʋ - φ₀     this equation called as Einstein’s photoelectric equation.

 Observation from equation-

• Kmax depends linearly on frequency ʋ , and is independent of intensity of radiation
• Kmax must be positive, impliesthat photoelectric emission is possible only if

               hʋ > φ0     or  ʋ > ʋ_o  where  ʋ_o = φ₀ /h           

• Threshold frequency is directly proportional to work function.
• In this picture, intensity of radiation is proportional to number of energy quanta perunit area per unit time. so greater the number ofenergy quanta available, the greater is the number ofelectrons absorbing the energy quanta andtherefore , greater number of electrons coming out ofthe metal (for ν > ν₀). This explains why, for ν > ν₀, photoelectric current is proportional to intensity.
• In Einstein’s picture, basic elementary process (absorption of a light quantum by a single
  electron) involved in photoelectric effect. This process is instantaneous. Thus, whatever may be intensity (the number of quanta of radiation per unit area per unit time) photoelectric emission is instantaneous.

• Intensity only determines how many electrons are able to participatein elementary process means photoelectric current.