Photoelectric Effect

Photoelectric Effect

• Atoms exist as positive ions within a sea of electrons in metals.
• Electrons near the metal's surface experience an inward attractive force due to the positive charges below.

Overcoming Inward Forces

• An electron has to perform a particular amount of work to escape the metal surface
• The work has to overcome the inward forces.

Photoelectric Emission

• Photoelectric emission involves releasing an electron from a metal surface using light of a certain frequency.

Thermionic Emission

• Thermionic emission involves releasing an electron from a metal surface using heat.
• Light supplies electrons with energy equal to or exceeding the energy binding them to the surface.

Photo Electrons

• Liberated electrons are called photoelectrons.

Photo Emissive Material

• Some surfaces that undergo electric emission are photo emissive, including K, Na, and Ca
• Group I elements generally exhibit this property
• These elements have low ionization energy or work function.

Demonstrating Photoelectric Effect

• A gold leaf electroscope and a suitable metal like zinc can demonstrate the photoelectric effect.

Laws of Photoelectric Emission

• These laws are from experimental results on the photoelectric effect.
• The time lag between irradiation of the metal surface and electron emission is negligible.
• A minimum radiation frequency, known as the threshold frequency (f0), must be met for photoelectrons to be emitted.
• Above the threshold frequency, the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
• Photoelectron kinetic energy is independent of the incident radiation intensity but depends on its frequency.

Photoelectric Effect Demonstration

• A freshly cleaned zinc plate connects to a negatively charged gold leaf electroscope cap.
• Shining ultraviolet light onto the zinc plate results in the electroscope leaf gradually falling, which indicates both the zinc plate and electroscope lose charge.
• Lost charges are electrons, confirming the photoelectric effect.
• Using a positively charged electroscope results in no observable change because emitted electrons are immediately attracted back.

Planck's Quantum Theory

• Energy/radiation is emitted or absorbed in discrete packets called quanta.
• Energy exists in integral values (1, 2, 3…n), rather than fractional amounts.
• The energy E in a radiation quantum is proportional to the frequency f of the radiation: E ∝ f or E = hf.
• Planck's constant (h) equals 6.626 x 10-34Js.

Dimensions of Planck's Constant (h)

• h = (force x distance) / frequency
• [h] = ML2T-1

Electromagnetic Radiation & Wavelength

• For electromagnetic radiation, c = λf
• E = hc/λ
• Thus, energy is proportional to frequency and inversely proportional to wavelength.

Quantum Theory of Photoelectric Effect

• Light energy is emitted/absorbed in packets called photons.
• A photon delivers energy or quanta of hf where f is light/radiation frequency and h is Planck's constant.
• Photons knock off electrons on the metal surface.
• When a photon collides with an electron:
  • It reflects without changing energy or gets absorbed.
  • Upon absorption, the photon gives its entire energy to a single electron without sharing.
• Work function (w0) is the energy required to eject an electron from a particular metal surface.
• Work function is characteristic to the metal, and is supplied by incident radiation.
• A photon of energy E (hf) causes electron emission from the metal surface.
• If 𝐸 > 𝑤_0, the excess energy becomes the kinetic energy of the emitted electron (photoelectron).
• The equation hf – w0 = ½ mv2, known as Einstein's photoelectric equation, relates these parameters.
• "v" in the equation is the velocity of the emitted electron.
• Emitted electrons escape with velocities up to a maximum value that depends on:
  • The metal's work function (w0).
  • The frequency (f) of incident radiation.

Equations for Photoelectric Effect

• hf = energy of incident radiation of frequency, f
• w0 = work function of the metal, defined as the minimum energy to release an electron
• ½ mv2 = maximum kinetic energy of the emitted electron
• If a photon has just enough energy to liberate an electron, the emitted electron gains no kinetic energy.
• For a particular metal, work function (w0) is constant, which means there is a minimum frequency (threshold frequency, f0) for photoelectric emission.
• Minimum frequency can be expressed with w0= hf0
• It follows that h(f-f0) = ½ mv2.
• Also w0 = hf0 and f0 = c/λ0
• The work function can be expressed as hc/λ0
• When an electron with charge e is accelerated by a voltage V, it gains K.E = eV
• h(f – f0) = eV describes the relationship between energy frequency, and voltage.
• An electron volt (eV) is the K.E gained by an electron accelerated through one volt (1eV = 1.6 x 10-19J).
• Constants include: h = 6.64 x 10-34Js, c = 3.0 x 108ms-1, e = 1.6 x 10-19C.

Photoelectric Emission Definitions

• Threshold Wavelength: This is maximum wavelength required to emit electrons from a metal surface.
• Threshold Frequency: This is the minimum frequency needed for the emission of electrons from the metal surface.

Calculating Kinetic Energy

• When monochromatic radiation of 1.0 x 1015 Hz frequency hits a magnesium surface with a work function of 0.59 x 10-18J, the emitted electrons have a maximum kinetic energy of 7.4 x 10-20J.

Calculating Potential

• The potential to raise the same magnesium surface to prevent escape of electrons is 0.46V.

Calculating Cut-Off Wavelength

• The Cut-off wavelength for magnesium is 3.38 x 10-7m, using the same data.

Calculating Work Function

• Calcium, having a work function of 2.7eV, has a work function of 4.3 x 10-19J from 2.7eV = 2.7 x 1.6 x 10-19.

Calculating Threshold Frequency

• The threshold frequency of calcium is 6.5 x 1014Hz derived from hfo = 4.3 x 10-19, 6.64 x 10-34 x fo = 4.3 x 10-19..

Calculating Maximum Wavelength

• Calcium's maximum wavelength that will cause emission is 4.6 x 10-7m
• λo = c/fo, 3 x 108 / 6.5 x 1014

Calculating Work Function for Metal Surface with Incident Light

• Given light frequency 6 x 1014Hz and kinetic energy of emitted electrons 2 x 10-29J, metal work function is 3.978 x 10-19J.
• Based on the equation hf = wo + ½ mv².

Calculating Threshold Frequency of Metal

• The threshold frequency of the metal is 6 x 1014Hz derived from wo = hfo.

Calculating Speed of Photoelectrons from Cesium Surface

• Maximum speed of photoelectrons emitted by Cesium when work function is 3 x 10-19J and wavelength is 484mm is 4.938 x 105ms-1.
• Equations for calculation include: (c = 3 x 108ms-1, h= 6.63 x 10-34Js, Me = 9.1 x 10-31kg).

Einstein's Photoelectric Equation & Planck's Constant Experiment

• Known-frequency radiation is directed at the photocathode.
• Emitted electrons travel to the anode, resulting in a detectable current at E.
• Potential difference V is adjusted until the anode current stops (reading of E becomes zero).
• This p.d value, the stopping potential (Vs), is noted from voltmeter V.
• Repeated with different light frequencies f to make graph.

Graph of Stopping Potential vs. Frequency

• The slope yields h/e, thus h = Se.

Stopping Potential

• The minimum potential between cathode and anode which prevents most energetic electrons from reaching the anode.

Experiment to measure Stopping Potential for a Metal Cell

• Anode (A) is made negative in potential relative to Cathode(C)
• Photoelectrons are emitted from C when illuminated with a beam, they experience a retarding potential
• Anode potential is increased negatively until the current flow stops becoming zero, and the stopping potential is noted via Voltmeter

Sodium and its Threshold Frequency

• Sodium, with a work function of 2.3eV, has a threshold frequency of 5.55 x 1014Hz determined by dividing the work function by Planck's constant.

Stopping Potential of Sodium

• Illuminated by a 5 x 10-7m wavelength light, sodium's stopping potential is 0.186V.
• (1eV = 1.6 x 10-19J)

Quantum Theory - Explaining Laws

• Quantum theory emits and absorbs light in photons.
• When light strikes a metal surface, each photon either interacts with a single electron and gives all its energy to it.
• If the energy is too low or The photon is absorbed, if its energy is greater than the work function

Intensity & Photons

• The numbers of photons will increase when higher intensity on the light is exerted.
• Increasing photons increases more electrons which in turn increase photocurrent.
• Increasing intensity of light effects more photons not the energy of electrons.
• Kinetic energy does not depending on the intensity of the strike

Limitations of Wave Theory

• Threshold Frequency Absent in Wave Theory: Classical theory would suggest that radiation with enough intensity would cause emission regardless of frequency, contradicting observed threshold frequency.
• Instantaneous Emission: Classical theory suggests that electron emission would take time as electrons accumulate energy contradicting instantaneous emission

Failures of Wave Theory to explain Kinetic Energy & Intensity

Classical theory predicts emitted photoelectrons' kinetic energy would increase with incident radiation intensity, but photoelectric emission has kinetic energy dependent on incident radiation's frequency.

• Classical theory increase would happen with intensity of emitted electrons but they would escape with greater speed instead which is false according to the observations

Electrical Current in Photocell & Photocells Description & types

• Thin Anodes & Vacuum Chambers characterize Photocells.
• Radiation Converted into Electrical Current via Photocells
• Cathode emits electrons when radiation strikes, anode collects the released ions to cause a current and this is caused by having an anode electrode
• Three distinct types consist of Photo emissive, Photovoltaic and Photoconductive electrodes

Photo Emissive Device

• Electrons emitted when radiation with high frequency is incident & moves to anode in closed circuit.
• Current will also depend on radiation of incident
• If light beaming is disturbed and stopped then the electrical current will cease to continue
• Uses of closed relay circuit which activate different things like door opening.

Photo-Voltaic

It creates e.m.f depending on incident of radiation with solar panels and calculators

Photoconductive

Material which is semiconductor is place inside a bulb and when the bulb is illuminated it is possible for to produce electric through it

Photoelectric experiments

• Monochromatic high constant light is applied
• By measuring intensity with constant variable voltages
• Polarity switch to opposite position during reversed value

Radiation

• Experiment repeat when increasing intensity as it move light closer
• It helps graphs and intensity to see what is the electrical reading
• Zero current electrical current doesn't means there is no current as electrons of high speed still travel in circuits

Relationship between Photoelectric and V Graph

• The energy depends on electrons and how quickly they can take in and overcome repulsive power