Quantum Physics : Gate Academy

Particle Model: Objects that are hard, have mass and move about according to the laws of Newtonian mechanics
Wave Model: They are shaped like a sine graph, do not have mass or charge. their defining characteristics are diffraction and interference

Photoelectric Effect: When an electromagnetic radiation of sufficiently high frequency falls on a metal surface, electrons are emitted
Delocalized electrons in metal are removed by supplying a small amount of energy provided by the incident electromagnetic radiation
Emitted electrons are called photoelectrons
Photoelectric Current: Current due to photoelectrons

- The first is a positively charged electroscope
- The second, a negatively charged electroscope
Positively Charged: When the zinc plate is exposed to u.v., the leaf remains open because though electrons are emitted, that are attracted back due to the +ve charge on zinc plate
Negatively Charged: When the zinc plate is exposed to u.v., the leaf slowly collapses as electrons are emitted, hence, -ve charge on the electroscope decreases
Laws of Photoelectric Emission:
- First Law: The number of photo-electrons emitted per second is directly proportional to the intensity of the incident radiation
- Second Law: The maximum kinetic energy of photo-electrons is directly proportional to the frequency of the incident radiation but independent of its intensity
- Third Law: For every metal, there is a minimum frequency of incident radiation below which photo-electric emission does not take place; it is called the threshold frequency
- Threshold Frequency: It is the minimum frequency required to release electrons from the surface of a metal

The energy of an electromagnetic wave does not flow continuously but in discrete quanta
Photon: Each quantum (particle) of electromagnetic radiation
Energy of a photon of an electromagnetic radiation of frequency f is given by
- E = hf
- where h is the Planck’s constant = 6.63 × 10^-34 Js
Work Function (Φ): The minimum amount of energy required by an electron to escape its surface
For a given frequency, electrons are emitted with a range of k.e. because electrons deeper inside the metal lose energy in collision with atoms as they are emitted

hf = Φ₀ + E_max
where Φ₀ is the work function of the metal
Thus, the energy of the absorbed photon is partly used to release the electron from the metal and partly to give it a kinetic energy
- hf = hf₀ + ½mv²_max

Wave Behavior: Electromagnetic radiation shows properties of diffraction and interference
Particle Behavior: Photo-electric effect
Thus electromagnetic radiations have a dual nature and their particles are photons

de Brogile suggested since waves can behave like particles, particles should be able to behave like waves
Matter Wave: A moving particle pf matter of momentum p will have an associated wave of wavelength λ, where λ = ^h/_p = ^h/_mv
- where h is Planck’s constant
- m is the mass
- v is the velocity of the particle
- λ is the de Brogile wavelength
Diffraction of Electrons:
- When a beam of electrons strikes a thin carbon foil, a diffraction pattern is obtained on a screen
- When the velocity of the electrons in a bean was increased by increasing the voltage, the rings in the pattern became narrower, showing the wavelength decreases as the velocity is increased, agreeing with de Brogile’s equation

The energy of an atom is the total energy of its electrons
Under normal conditions, an atom is in its ground state where it possesses the minimum possible energy
When the atom absorbs energy, the energy of the atom increases and the atom is in an excited state
The excited state is unstable, so the atoms eventually emit absorbed energy, bringing the atom back to its ground state
Transition: is the shifting of electrons between energy levels
Electrons release energy in the form of electromagnetic radiation
The frequency of the emitted radiation is given by:
- hf = E₂ – E₁
- where f is the frequency,
- E₂ is the energy of the higher level, and
- E₁ is the energy of the lower level
The frequencies of the electromagnetic radiation emitted by electrons when they come down to their ground state were found to be discrete, showing electrons can only absorb certain discrete values, therefore the energy of an atom is quantized

Emission Line Spectra: The composition of light emitted by a hot gas
- The frequencies emitted by the atoms of a substance when they de-excite from higher to lower energy levels
Absorption Line Spectra: When white light is passed through a cool gas
- The frequencies absorbed from a continuous spectrum by the electrons
The emission and absorption spectra are characteristic of each element

Atoms in solids are close together and electrons from one atom interacts with those of neighboring atoms, altering energy level diagrams
An electron can have an energy at any level in one of the energy bands
However, it cannot have an energy which lies in the forbidden gap

In a metal, the conduction band is only partially filled with free electrons which gives the metal is conductivity
In an insulator, the conduction band is unoccupied and the valence band is fully occupied
In a metal, the conduction band overlaps with the valence band allowing it to conduct electricity
- When a metal is heated, resistance increases because there is no increase in density of electrons in the conducting band; instead atoms vibrate more and electrons collide more frequently
In an insulator, there is a large forbidden gap between the valence and conduction band and voltage is insufficient to lift electrons across
In an intrinsic semiconductor, its conduction band is also empty, however, the gap between the two is very small
- When heated, electrons gain energy to jump into the conduction band and the material will conduct better
In an LDR, photons of light are absorbed by electrons in valence bands so they jump the gap into the conduction band