Definitions [15]
Define threshold frequency.
The minimum frequency of incident radiation required to start photoemission in any photosensitive material is known as the threshold frequency.
An electron volt is the energy gained by an electron when it is accelerated through a potential difference of 1 volt.
1 eV = 1.602 × 10−19J
Define the work function of a metal. Give its unit.
The minimum energy needed for an electron to escape from the metal surface is called the work function of that metal. Its unit is electron volt (eV).
The phenomenon of emission of electrons from the metal surface is called "Electron Emission".
The minimum energy required by an electron to escape from the surface of a metal is called the work function (ϕ0) of that metal.
Unit: electron volt (eV).
It is a phenomenon where light falling on a material (usually a metal) causes it to emit electrons, generally called photoelectrons.
The emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency falls on it. This phenomenon is called the photoelectric effect.
The minimum frequency of incident radiation required to just cause photoelectric emission from a given metal is called the threshold frequency.
Electrons emitted from the metal during photoelectric emission are called photoelectrons.
Define the term: stopping potential in the photoelectric effect.
The stopping potential is defined as the potential necessary to stop any electron from reaching the other side.
Define the term: threshold frequency
Threshold frequency is the lowest frequency of electromagnetic radiation that will result in the emission of electrons from a specified metal surface.
The photoelectric effect demonstrates that light behaves as if it consists of energy packets called quanta or photons.
The property by which light or matter can show both wave-like and particle-like behaviour depending on the experiment is called wave-particle duality.
The waves associated with a moving material particle are called matter waves or de Broglie waves.
According to de Broglie, every moving particle is associated with a wave whose wavelength depends on its momentum.
Formulae [2]
E = hν
where:
- E = energy of one photon
- h = Planck’s constant = 6.626 × 10-34 J s
- ν = frequency of radiation
For a particle of momentum p, the associated wavelength is:
For a particle of mass m moving with speed v:
- λ = de Broglie wavelength
- h = Planck's constant
- p = momentum of the particle
- m = mass of the particle
- v = velocity of the particle
Key Points
- Maxwell’s equations and Hertz’s experiments established the wave nature of light.
- Low-pressure discharge tube experiments led to important discoveries in atomic structure.
- Cathode rays were identified as fast-moving negatively charged particles.
- J. J. Thomson measured the specific charge of these particles and named them electrons.
- Millikan measured the elementary charge and established the quantisation of electric charge.
- Photoelectric emission was discovered in 1887 by Heinrich Hertz.
- Hertz made this observation during electromagnetic wave experiments.
- High-voltage sparks across the detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.
- Light shining on the metal surface facilitated the escape of free, charged particles.
- These free, charged particles are electrons.
- Electrons near the metal surface absorb energy from incident radiation.
- If the absorbed energy is sufficient, electrons overcome the attraction of positive ions in the material.
- The electrons then escape from the metal surface into the surrounding space.
de Broglie Wavelengths for Charged Particles (accelerated through potential V)
| Particle | Mass | de Broglie Wavelength |
|---|---|---|
| Electron | me = 9.1 × 10−31 kg | \[\lambda=\frac{12.27}{\sqrt{V}}\] Å |
| Proton | mp = 1.67 × 10−27 kg | \[\lambda=\frac{0.286}{\sqrt{V}}\] Å |
| Deuteron | md = 2 × 1.67 × 10−27 kg | \[\lambda=\frac{0.202}{\sqrt{V}}\] Å |
| α-particle | mα = 4 × 1.67 × 10−27 kg | \[\lambda=\frac{0.101}{\sqrt{V}}\] Å |
de Broglie Wavelengths for Uncharged Particles:
| Particle/Condition | Formula |
|---|---|
| Neutron | \[\lambda=\frac{h}{\sqrt{2mK}}=\frac{6.62\times10^{-34}}{\sqrt{2\times1.67\times10^{-27}K}}\] |
| Thermal neutron (at temp T) | \[\lambda=\frac{h}{\sqrt{2mkT}}=\frac{30.835}{\sqrt{T}}\] Å |
| Gas molecules at temp T | \[\lambda=h/mv_{rms},\mathrm{energy~}K=\frac{3}{2}kT\to\lambda=\frac{h}{\sqrt{3mkT}}\] |
Key Derivation Logic:
- Planck's quantum theory: photon energy E = hν, de Broglie wavelength λ = h/p
- If a photon has energy E = hν, treating it as mass m by relativity: E = mc2, so p = mc = h/λ
- For a material particle: momentum p = mv, so de Broglie wavelength λ = h/(mv)
- Kinetic energy \[K=p^2/2m\to\lambda=h/\sqrt{2mK}\]
Concepts [11]
- Understanding Dual Nature of Radiation and Matter
- Electric Discharge Through Gases
- Electron Emission
- Photoelectric Effect - Hertz’s Observations
- Photoelectric Effect - Hallwachs’ and Lenard’s Observations
- Experimental Study of Photoelectric Effect
- Photoelectric Effect and Wave Theory of Light
- Einstein’s Photoelectric Equation: Energy Quantum of Radiation
- Particle Nature of Light: The Photon
- Wave Nature of Matter
- De Broglie's Explanation
