Quantum phenomena

B- decay

The process where a d quark transforms into a u quark.

B+ decay

The process where a u quark transforms into a d quark.

Conservation laws

Energy and momentum are conserved in interactions.

Photon energy equation

Photon energy can be calculated using hf or hc/λ.

Work function (ϕ)

The minimum energy needed to release an electron from the surface of a metal.

Condition for electron release

An electron is released if hf ≥ ϕ.

Maximum kinetic energy

The remaining energy of an electron after the photoelectric effect

Threshold frequency (f0) and formula

Where photons have just enough energy to provide the work function energy, f0 = ϕ/h.

Photoelectric equation

The relationship given by hf = ϕ + KEmax.

Stopping potential

The potential difference needed to stop the fastest moving electrons.

Electronvolt

The energy gained by an electron moved through a potential difference of 1V.

Ionisation

The removal of an electron from an atom.

Excitation

The gain of energy by an electron to be promoted to a higher energy level.

Fluorescent tubes

high voltage applied to tube accelerates fast moving electrons that ionise mercury atoms, producing more free electrons

free electrons collide with electrons in other mercury atoms

mercury atoms gain energy through electron impact, exciting electrons

mercury atoms emit UV photons through de-excitation

coating on inside of tube absorbs UV photos, exciting its electrons

these electrons de-excite and emit lower energy photons to form visible light

Line spectra and energy levels

Electrons in atom only exist in certain well-defined energy levels

Electrons de-excite and emit photons

Since these transitions are between definite energy levels, only certain energy changes allowed

So the energy of each photon emitted can only take a certain allowed value, which corresponds to a specific wavelength

Light with this specific wavelength is a line on a spectrum

Smaller ΔE means..

Longer wavelength, smaller frequency

Why is there KEmax + range

Photon energy is constant

Photon loses all energy in one interaction

Max obtained from hf - ϕ

Electrons beneath surface must do work to reach surface then ϕ is required → leaves less energy for KE once it is released hence range

Wave-particle duality in EM radiation

EM radiation has diffraction and interference patterns like waves but behaves like a particle in photoelectric effect

Wave-particle duality in electrons

Behave like waves in electron diffraction but like particles during deflection in magnetic fields

de Broglie wavelength formula

The wavelength associated with a particle is given by λ = h/mv.

De Broglie wavelength and momentum

Momentum increases, de Broglie wavelength decreases so the angle of diffraction in an electron diffraction pattern gets smaller

De Broglie wavelength understanding over time

First hypothesised to explain observations

Other scientists peer review before publication

Tested with experiments

Theory was accepted as validated by scientific community once enough evidence found

Peer review

The process by which other scientists evaluate a theory before publication.

Photon energy features

Photon energy is constant

If photons have less energy than ϕ, they cannot provide sufficient energy to release electrons

Electrons Vs protons

Electrons are easier to obtain and accelerate than protons

Wave theory

Predicts photoelectrons will be emitted with any frequency

Effect of intensity on photoelectrons

KE unchanged

Increasing intensity results in more photons per second as one photon interacts with one electron,

Increased number of interactions means number of electrons released per second increases

Current definition

Rate of flow of charge

Charge flow formula

Charge flow = current X time

Q = A x t

Mercury low pressure

keeps mercury as vapour

allows electrons to accelerate without being absorbed by nitrogen or oxygen

must be large distance between collisions to allow electrons to gain enough energy

Why doesn't light below f0 release electrons

Because photons carry quanta of energy

Work function units

The unit of work function is Joules (J).

Ionisation energy

The energy required to completely remove an electron from an atom in its ground state.

Ground state

The lowest energy state of an atom.

Fluorescence

The absorption of high energy (UV) photons and emission of lower energy (visible) photons.

Momentum (p) formula

The formula for momentum is p = mv, where m is mass and v is velocity.

Units of momentum

The units of momentum are kg·m/s.

Particle diffraction conditions

A particle will diffract when its de Broglie wavelength is roughly the same size as the object causing the diffraction.

Equations for finding speed of electron

KEmax = ½mv²

Or

v = √(2eV/m) where e is the charge of an electron, V is the potential difference and m is the mass of an electron

Work done by an electric field formula

E = VQ where E is work done, Q is charge and V is potential difference

why are energy levels negative?

because to remove an electron, energy must be supplied

once free, an electron has zero energy

why is mercury vapour kept at low pressure

mercury vapour kept at low pressure is conducting so electrons can move through vapour

equation for stopping potential

Vstop = KEmax / e (charge of an electron)