Atoms and Quanta definitions

Quantum physics

The study of very small matter and energies

Faraday’s Law

The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic field enclosed by the circuit.

Maxwell’s Laws

1) A time-varying magnetic field acts as a source of electric field.

2) A time-varying electric field acts as a source of magnetic field.

Conduction

 takes place within an object or material, or between two objects that are in direct/ indirect contact with each other

Convection

 is the transfer of heat from one place to another by the movement of fluids

Thermal Radiation

 Interatomic collisions cause the kinetic energy of the atoms to change, resulting in the charge acceleration of the electrons, which in turn produces electromagnetic radiation over a wide range of wavelengths.

Blackbody

Blackbodies are idealised objects that emit thermal spectra of a universal character.

The work function

The threshold of energy a photon needs to have for a photoelectron to be released

Compton shift

The shift in wavelength of one of the 2 peaks of scattered X rays varies with the angle at which the scattered x-rays are observed.

What is the wave pattern?

A measure of the probability of detecting a photon at that point

Wave-particle duality

The suggestion that every particle or quantum entity can be described as both a wave and a particle in some phenomena

The principle of complementarity

Without considering both wave and particle properties, you cannot describe a particle or a photon completely. Moreover, these wave and particle properties cannot be observed simultaneously

Heisenberg Uncertainty principle

It is not possible to make a simultaneous determination of the position and the momentum of a particle with unlimited precision

It is not possible to make a simultaneous determination of the energy and time coordinate of a particle with unlimited precision

Schrodinger wave function

A mathematical function which contains all the information about a microscopic system

Boundary conditions for the Schrodinger equation

1) The wave function must be continuous

2) The slope of the wave function must be continuous (the derivative of the wave function must be the same on both sides) except when the wave function is infinite

Atomic line emission spectra

The unique results of forcing an electric discharge in a tube containing a small amount of gas or vapour of one element where light of a few discrete wavelengths are emitted

Atomic line absorption spectra

When we pass a light source through a gas, we find that certain wavelengths have been absorbed from the light, and again, a line spectrum results. 

Balmer series

The specific emission of visible wavelengths for hydrogen

Lyman series

The specific emission spectra of the ultraviolet wavelengths for hydrogen

Frank-hertz experiment procedure(1914)

• To prove that atoms have discrete energy levels for electrons

• Filled a glass tube at low pressure with Mercury Vapour

• Heat a cathode C using a filament which emits electrons

• Accelerate emitted electrons with applied potential V onto anode G

• Measure the current reaching P with an ammeter

Frank-Hertz Experiment (1914) results

• Initially current gradually increases with Voltage as there is no interaction with the gas other than elastic scattering

• At 4.88 V sudden drop in the current due to inelastic collisions between electrons and mercury atoms caused the atoms to excite to their first excited state

• Current again increases until the electron has high initial energy to excite two atoms in two successive collisions.

• At 9.76 sudden drop in current due to electrons exciting two atoms

• Cycle continues for 3 atoms excited

Bohr Theory of atom

Miniature planetary system, with electrons circulating the nucleus like planets circling the sun. Where the electrons are in a ‘stationary state’ and, therefore, don’t emit electromagnetic radiation.

5 quantum numbers

1. how far the orbital is from the nucleus (n) values of 1,2,3,4…

2. how fast the orbit is (angular momentum) (l) value of n-1 (If n=4, l must be 3)

3. the angle of the orbit in space (m_l) values between and including -l and +l (if l = 2 , ml = -2,-1,0,1,2)

4. intrinsic angular momentum of the electron (s) value of ½

5. direction of spin of electron (m_s) value of ½ or -1/2 depending on if it spins left or right

for a non-uniform magnetic field (inhomogeneous)

1) if the magnetic dipole is aligned with the external field it seeks a higher field ( if the moment points up, net force points down)

2) If the dipole is anti-aligned it seeks a lower field ( if the moment is angled down, net force points up)

Stern-Gerlach

• Wanted to prove spatial quantisation

• fired a beam of silver atoms through collimating slits into a non-uniform magnetic field

• atoms were prepared in the n=2, l=1 state

• expected 3 images on the glass plate characterised by m_l = -1,0,1

• instead, only two images were returned, which would suggest l=1/2, which is not possible

• this is because intrinsic spin was needed to explain.

Fine structure splitting

The fact that most spectral lines can be split into two smaller spectral lines when using more accurate equipment

Spin-orbit coupling

The cause of fine structure splitting - the interaction of the electron's intrinsic spin angular momentum and the orbital angular momentum

Zeeman Effect

1896 - Pieter Zeeman was able to split spectral lines with the application of an external magnetic field, resulting in multiples of spectral lines (some of which he could not explain due to lack of knowledge of spin)

Why can influential forces not be separated into more or less influential in an atom?

The effect from the nucleus is comparable with the effect of all the other electrons and, therefore, cannot be analysed separately.

Spectroscopic notation to label energy levels

each l value is designated a letter:

l=0,1,2,3,4,5,6 corresponds to l=s,p,d,f,g,h,i respectively

an energy level is denoted by its value of n and letter of all next to each other

e.g. when n=1, l=0 is the 1s state

By what values can l change when a transition of energy levels occur?

± 1

e.g. from an energy state of 4p (n=4, l=1) electron can move down to 3s, 3d, 2s, 1s

Atomic shells

States with the same value of n (have approx. same energy)

Labelled as: K, L, M, N, O… for n=1,2,3,4,5…

Atomic subshells

States with the same value of n and l (can have different values of m_l)

Pauli Exclusion Principle

No two electrons in a single atom can have the same set of quantum numbers (n, l, m_l, m_s)

What is electron screening?

The effect in which inner electrons shield the charge of the nucleus from outer electrons.

Two main principles of properties of electrons:

1) Filled subshells are normally very stable configurations

2) Filled subshells do not normally contribute to the chemical or physical properties of an atom.

4 properties of elements and main findings

1 Atomic Radii - Atoms with larger nucleus charges have shrinkage in the p shell due to the nucleus pulling electrons closer

2 Ionisation Energies - Atoms with entirely filled subshells (Inert gases, Helium, Neon etc. ) have much higher Ionisation energies due to the extra energy needed to break open shells

3 Resistivity - Good electrical conductors have low resistivity and loosely bound electrons that can flow as delocalised electrons

4 Magnetism - Magnetic properties of the Lanthanides are even stronger than the transition metals due to the larger angular momentum of f subshell

What happens when inner electrons are displaced due to far more energy being inputted?

Characteristic X rays are emitted in transitions between the more tightly bound inner electron levels of an atom

What is the most striking feature of X-ray line spectra and why?

The frequencies and wavelengths of lines vary smoothly from element to element

as they are dependent on binding energies of inner electrons which increase uniformly with atomic number Z

Moseley’s Law

The dependency of X-ray Energies on atomic number Z