Cathode Rays: Properties and Discoveries

• Maxwell's equations and Hertz's experiments in 1887 established light's wave nature.
• Late 19th-century experiments on electric discharge through gases led to historic discoveries.
• Roentgen's discovery of X-rays in 1895 and Thomson's discovery of the electron in 1897 were milestones in atomic structure.
• A discharge occurs between electrodes in a discharge tube at low pressure (0.001 mm of mercury column) when an electric field is applied.
• A fluorescent glow appears on the glass opposite the cathode; its color depends on the glass type (yellowish-green for soda glass).
• The radiation from the cathode causes fluorescence.
• William Crookes discovered cathode rays in 1870 that consist of streams of fast-moving, negatively charged particles.
• British physicist J.J. Thomson (1856-1940) confirmed the cathode ray hypothesis.
• J.J. Thomson experimentally determined the speed and specific charge (e/m) of cathode ray particles using electric and magnetic fields.
• Cathode ray particles travel at speeds of about 0.1 to 0.2 times the speed of light (3 × 10^8 m/s).
• The currently accepted value of e/m is 1.76 × 10^11 C/kg.
• The e/m value is independent of cathode material or gas in the discharge tube, suggesting the universality of cathode ray particles.
• In 1887, metals irradiated by ultraviolet light emit negatively charged particles with small speeds.
• Certain heated metals emit negatively charged particles.
• The e/m value of these particles matches that of cathode ray particles, establishing their identical nature despite different production methods.
• J.J. Thomson named these particles electrons in 1897, suggesting they're fundamental, universal matter constituents.
• Thomson was awarded the 1906 Nobel Prize in Physics for his electron discovery.
• R.A. Millikan (1868-1953) performed the oil-drop experiment in 1913 to precisely measure electron charge.
• An oil droplet's charge is always an integral multiple of an elementary charge, 1.602 × 10^-19 C, establishing that electric charge is quantized.
• The electron's mass can be determined from the values of charge (e) and specific charge (e/m).

Electron Emission

• Metals contain free electrons which are negatively charged and responsible for conductivity.
• Free electrons cannot normally escape the metal surface.
• When an electron tries to escape, the metal surface becomes positively charged, pulling the electron back.
• Electrons are held inside the metal by the attractive forces of ions.
• An electron requires sufficient energy to overcome the attractive pull to escape the metal surface, this minimum energy is called the work function (𝜙0)
• Work function is measured in electron volts (eV).
• One electron volt is the energy gained by an electron accelerated by a 1-volt potential difference: 1 eV = 1.602 × 10^-19 J.
• Electron emission from a metal surface can be achieved by:
• Thermionic emission: Heating the metal to impart sufficient thermal energy to free electrons, allowing them to escape.
• Field emission: Applying a strong electric field (≈ 10^8 V/m) to pull electrons out of the metal.
• Photoelectric emission: Illuminating the metal surface with light of suitable frequency, causing the emission of photoelectrons.

Photoelectric Effect

• Heinrich Hertz discovered the photoelectric emission phenomenon in 1887 during electromagnetic wave experiments
• High voltage sparks across a detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.
• Light shining on a metal surface facilitates the escape of free, charged particles now known as electrons.
• When light strikes a metal surface, electrons near the surface absorb energy from the radiation, overcoming the attraction of positive ions.
• After gaining sufficient energy, the electrons escape from the metal into the surrounding space.

Hallwachs' and Lenard's Observations

• Wilhelm Hallwachs and Philipp Lenard investigated photoelectric emission in detail from 1886-1902.
• Lenard observed that ultraviolet radiation on the emitter plate of an evacuated glass tube caused current flow.
• When the ultraviolet radiation stopped, current flow stopped which indicates electrons are ejected from the emitter plate C and are attracted to the positive collector plate A by the electric field.
• Electrons flow through the evacuated tube, resulting in current in the external circuit, thus light falling on the emitter causes current in the external circuit.
• Hallwachs and Lenard studied how photocurrent varied with collector plate potential, frequency, and intensity of incident light.
• In 1888, Hallwachs connected a negatively charged zinc plate to an electroscope and observed that the zinc plate lost its charge when illuminated by ultraviolet light.
• The uncharged zinc plate became positively charged when irradiated by ultraviolet light.
• Positive charge on a positively charged zinc plate was further enhanced when illuminated by ultraviolet light.
• Negatively charged particles were being emitted from the zinc plate with ultraviolet exposure.
• The incident light causes electrons to be emitted from the emitter plate.
• Emitted electrons are pushed towards the collector plate by the electric field due to their negative charge.
• When ultraviolet light fell on the emitter plate, no electrons were emitted if the incident light's frequency was below a minimum value called the threshold frequency.
• Threshold frequency depends on the emitter plate's material.
• Certain metals (zinc, cadmium, magnesium) respond only to ultraviolet light with short wavelengths to cause electron emission.
• Alkali metals (lithium, sodium, potassium, caesium, rubidium) are sensitive even to visible light.
• Photosensitive substances emit electrons when illuminated by light and these electrons are called photoelectrons.
• The phenomenon is called the photoelectric effect.

Experimental Study of Photoelectric Effect

• A schematic view of the arrangement used for the experimental study of the photoelectric effect includes an evacuated glass/quartz tube having a thin photosensitive plate C and another metal plate A.
• Monochromatic light from source S of sufficiently short wavelength passes through window W and falls on the photosensitive plate C (emitter).
• A transparent quartz window is sealed onto the glass tube that permits ultraviolet radiation to irradiate the photosensitive plate C.
• Electrons emitted by plate C are collected by the plate A (collector), by the electric field created by the battery.
• The battery maintains the potential difference between plates C and A, that can be varied
• The polarity of plates C and A can be reversed by a commutator, thus plate A can be maintained at a desired positive or negative potential with respect to emitter C.
• When the collector plate A is positive with respect to the emitter plate C, the electrons are attracted to it.
• The emission of electrons causes flow of electric current in the circuit.
• The potential difference between the emitter and collector plates is measured by a voltmeter (V).
• The resulting photocurrent flowing in the circuit is measured by a microammeter (µA).
• Photoelectric current can be increased or decreased by varying the potential of the collector plate A with respect to the emitter plate C.
• Varying the intensity and frequency of the incident light can vary the potential difference V between the emitter C and the collector A.
• The experimental arrangement can study the variation of photocurrent with:
  • Intensity of radiation.
  • Frequency of incident radiation.
  • Potential difference between plates A and C.
  • Nature of the material of plate C.
• Light of different frequencies can be used by putting appropriate coloured filter or coloured glass in the path of light falling on the emitter C, varying the distance of the light source can vary the intensity.

Effect of intensity of light on photocurrent

• Collector A is kept at a positive potential relative to emitter C, attracting the ejected electrons.
• With a fixed incident radiation frequency and potential, varying the light intensity alters the resulting photocurrent.
• Photocurrent increases linearly with incident light intensity.
• Photocurrent is directly proportional to the number of photoelectrons emitted per second.
• Number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

Effect of Potential on Photoelectric Current

• Plate A is kept at some positive potential relative to plate C and plate C is illuminated with light of a fixed frequency ν and a fixed intensity I1.
• Gradually varying the positive potential of plate A measures the resulting photocurrent each time.
• Photocurrent increases with an increase in positive (accelerating) potential until a certain point.
• At a certain positive potential of plate A, all emitted electrons are collected by plate A and the photoelectric current becomes maximum or saturates.
• Increasing the accelerating potential of plate A further does not increase the photocurrent; this maximum value is called saturation current.
• Saturation current corresponds to the case when all the photoelectrons emitted by the emitter plate C reach the collector plate A.
• A negative (retarding) potential is applied to plate A with respect to plate C.
• The electrons are repelled while only the sufficiently energetic electrons will reach the collector A.
• The photocurrent decreases rapidly until it drops to zero at a sharply defined, critical value of the negative potential V0 on plate A.
• Minimum negative (retarding) potential Vo required to stop the photocurrent (make it zero) is called the cutoff or stopping potential for a particular frequency of incident radiation.
• The interpretation in terms of photoelectrons is straightforward which states all photoelectrons emitted from the metal do not have the same energy.
• Photoelectric current is zero when the stopping potential is sufficient to repel the most energetic photoelectrons, with the maximum kinetic energy (Kmax), so that:
• Kmax = e Vo
• Repeating the experiment with incident radiation of the same frequency but of higher intensities I2 and I3 (I3 > I2 > I1) shows that the saturation currents are now found to be at higher values.
• More electrons are being emitted per second, proportional to the intensity of incident radiation.
• The stopping potential remains the same shown in Fig. 11.3 for the incident radiation of intensity I1.
• For a given frequency of the incident radiation, the stopping potential is independent of its intensity.
• Maximum kinetic energy of photoelectrons depends on the light source and the emitter plate material, yet is independent of intensity of incident radiation.

Effect of Frequency of Incident Radiation on Stopping Potential

• The relation between the frequency ν of the incident radiation and the stopping potential V0 can be studied by adjusting the same intensity of light radiation at various frequencies.
• Study the variation of photocurrent with collector plate potential. The resulting variation is shown in Fig 11.4.
• Different values of the stopping potential can be obtained but the same value of saturation current is obtained for an incident radiation of different frequencies.
• The energy of the emitted electrons depends on the frequency of the incident radiation.
• The stopping potential is more negative for higher frequencies of incident radiation.
• The stopping potentials are in the order of V03 > V02 > V01 if the frequencies are in the order v3 > v2 > v1 shown in Fig 11.4.
• This implies that the greater the frequency of incident light, the greater is the maximum kinetic energy of the photoelectrons.
• Greater retarding potential is needed to stop the photoelectrons completely.
• To plot a graph between the frequency of incident radiation and the corresponding stopping potential for different metals gives a straight line illustrated in Fig 11.5.
• The graph shows that:
  • The stopping potential Vo varies linearly with the frequency of incident radiation for a given photosensitive material.
  • There exists a certain minimum cutoff frequency vo for which the stopping potential is zero.
• Two implications of these observations are:
  • The maximum kinetic energy of the photoelectrons varies linearly with the frequency of incident radiation, yet is independent of its intensity.
  • For a frequency ν of incident radiation, lower than the cutoff frequency ν0, no photoelectric emission is possible even if the intensity is large.
• Minimum, cutoff frequency ν0, is called the threshold frequency and differs for different metals.
• Photosensitive materials respond differently to light and selenium is more sensitive than zinc or copper.
• The same photosensitive substance responds differently to light of different wavelengths, where ultraviolet light gives rise to photoelectric effect in copper while green or red light does not.
• In all the above experiments, it is found that, if the frequency of the incident radiation exceeds the threshold frequency, the photoelectric emission starts instantaneously, with no apparent time lag, even if the incident radiation is very dim.
• Emission starts in a time of the order of 10^-9 s or less.
• We can summarize the experimental features and observations which states:
  • For a given photosensitive material and frequency of incident radiation (above the threshold frequency), the photoelectric current is directly proportional to the intensity of incident light.
  • For a given photosensitive material and frequency of incident radiation, saturation current is often proportional to the intensity of incident radiation whereas the stopping potential is independent of its intensity.
  • For a given photosensitive material, a certain minimum cut-off frequency of the incident radiation, called the threshold frequency, exists below which no emission of photoelectrons takes place, no matter how intense the incident light is.
  • Above the threshold frequency, the stopping potential or equivalently the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation and is independent of its intensity.
  • The photoelectric emission appears to be an instantaneous process with no apparent time lag (~10^-9 s or less), even when the incident radiation is made exceedingly dim.

Photoelectric Effect and Wave Theory of Light

• The wave nature of light was well established by the end of the nineteenth century.
• Phenomena of interference, diffraction, and polarization were explained naturally and satisfactorily by the wave picture of light.
• Light is an electromagnetic wave with continuous energy distribution over the region of space over which the wave extends.
• According to the wave picture of light, free electrons at the metal's surface absorb radiant energy continuously.
• The greater the radiation intensity, the greater the electric and magnetic field amplitudes.
• Maximum kinetic energy of the photoelectrons on the surface should increase with increasing intensity.
• Sufficiently intense radiation should impart enough energy to electrons to exceed the minimum energy needed to escape the metal surface regardless of the radiation frequency so there should not be a threshold frequency.
• These expectations of the wave theory contradict observations (i), (ii), and (iii).
• In the wave picture, absorption of energy by electron takes place continuously over the entire wavefront of the radiation as many electrons absorb energy, the energy absorbed per electron per unit time turns out to be small.
• Picking up sufficient energy to overcome the work function and emerge out of the metal can take hours or more for a single electron.
• Explicit calculations estimate that it can take hours or more for a single electron to pick up sufficient energy to overcome the work function and come out of the metal.
• This conclusion contrasts with that the photoelectric emission is instantaneous.
• The wave picture is unable to explain the basic features of photoelectric emission.

Einstein’s Photoelectric Equation: Energy Quantum of Radiation

• In 1905, Albert Einstein proposed a new picture of electromagnetic radiation to explain the photoelectric effect, thus photoelectric emission does not take place by continuous absorption of energy from radiation.
• Radiation energy is formed of discrete units called quanta of energy of radiation also known as the radiation energy.
• Each quantum of radiant energy has energy hν, where h is Planck’s constant and ν the frequency of light.
• Photoelectric effect: an electron absorbs a quantum of energy (hν) of radiation.
• The electron is emitted with maximum kinetic energy Kmax = hν – Φ0 if the absorbed energy exceeds the minimum energy needed for the electron to escape the metal surface also is called the work function (Φ0).
• More tightly bound electrons will emerge with kinetic energies less than the maximum value.
• Intensity of light of a given frequency is determined by the number of photons incident per second.
• Increasing intensity increases the number of emitted electrons per second, however, the maximum kinetic energy of the emitted photoelectrons is determined by the energy of each photon.
• Known as Einstein's photoelectric equation, it accounts for photoelectric effect observations.
• According to Einstein’s theory, Kmax depends linearly on ν and is independent of radiation intensity.
• Einstein's photoelectric effect arises from the absorption of a single quantum of radiation by a single electron, so the radiation intensity that is proportional to energy quanta per unit area is irrelevant.
• Since Kmax must be non-negative where hν > Φ0 or ν > ν0,
  • then ν0 = Φ0 / h
• The greater the work function Φ0, the higher the minimum or threshold frequency ν0 needed to emit photoelectrons exists a threshold frequency ν0 (= Φ0 / h).
• No photoelectric emission is possible below the metal surface, no matter how intense the incident radiation or how long it falls on the surface.
• Intensity is proportional to the number of energy quanta per unit area per unit time and the greater the number of energy quanta available, the greater the number of electrons absorbing are able to participate.
• Then the number of electrons coming out of the metal is greater where ν > ν0 as it explains why, for ν > ν0, photoelectric current is proportional to intensity.
• Photoelectric effect is the absorption of light quantum by an electron which is instantaneous.
• The low intensity does not delay in low intensity emission although it only determines how many electrons absorb a light quantum resulting in photoelectric emission.
• Using Eq. (11.1), the photoelectric equation is,
  • e V0 = hν - Φ0 for ν ≥ ν0
    • V0 = h/e ν- Φ0/e.
• The Equation predicts that the Vo versus ν curve is a straight line with a slope of h/e.

Key People

• Millikan performed experiments in 1906-1916, aimed at disproving Einstein's photoelectric equation and measured the slope of the straight line obtained for sodium.
• Determined Planck's constant h and verified Einstein's photoelectric equation in 1916.
• Einstein: Introduced light quanta (photons) and explained the photoelectric effect, developed theory of Brownian motion, and gave birth to the special theory of relativity.
• Louis Victor de Broglie: Attributed a wave-like character to matter (material particles thus waves associated with moving particles are called matter waves or de Broglie waves).

Particle Nature of Light: The Photon

• Photoelectric effect provided evidence that light interacts with matter like packets of energy.
• Light quanta of energy can be associated with a particle that Einstein arrived at.
• Light quantum can also be associated with momentum (hν/c) and light quanta can be associated with a particle called a photon that was named later.
• The photon picture of electromagnetic radiation occurs as follows:
  • Radiation behaves as if it is made up of particles called photons during interaction with matter.
  • Each photon has energy E (=hν) and momentum p (= hν/c), and speed c, the speed of light.
  • All photons of light of a particular frequency ν, or wavelength λ, have the same energy and momentum.
    • Equation: p = hν/c = h/λ
  • By increasing the intensity of light of given wavelength, there is only an increase in the number of photons per second crossing a given area, with each photon having the same energy.
• Photon energy is independent of intensity of radiation.
• Photons are electrically neutral and are undeflected by electric and magnetic fields.
• The total energy and total momentum are conserved in a photon-particle collision (such as a photon-electron collision). However, the number of photons may not be conserved in a collision.