Atoms and Quanta definitions

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.

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.

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

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

Frank-hertz experiment procedure(1914)

Aim: To confirm that radiation is quantised

Procedure:

1. A glass tube filled with mercury vapour

2. Electrons emitted from the heated cathode

3. Accelerated towards the Anode grid

4. Current reaching the plate against the Voltage plotted

   Results: Current drops at multiples of 4.9v due to inelastic collisions exciting atoms from the ground state

Bohr model main 4 Assumptions

1. Discrete orbits and energies in ‘stationary states’

2. Classical mechanics describes these states

3. A single quantum of energy is released in a jump between states

4. allowed orbits determined by the quantisation of angular momentum

4 quantum numbers

Principle Quantum number - n

Angular Momentum Quantum Number - l

Magnetic Quantum number - m_l

Spin quantum number - m_s

Stern-Gerlach

Aim: To prove spatial quantisation

Procedure: Fired silver atoms (l=0) through a non-uniform magnetic field

Results: 2 images (suggesting l=1/2)

implying another contribution to angular momentum (intrinsic spin)

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

Interaction between the internal magnetic field of the atom and the intrinsic angular momenta of the electron.

The orbital momentum corresponds to an internal magnetic filed which interacts with the spin of the electron.

Zeeman Effect Cause

Interaction between the angular momentum of the electron and an external field.

4 properties of elements and main findings

1 Atoms with larger nuclear charges have a shrinkage in the p shell due to the nucleus pulling electrons closer

2 Ionisation Energies - Atoms with entirely filled subshells have much higher Ionisation energies due to the extra energy needed to break open shells

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

4 Magnetic properties are stronger due to the larger angular momentum of f subshell

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

Bremstrahlung Radiation

X-rays may be produced if electrons decelerate or stop in the target material

Electron collisions- X-ray

1. An electron collides with an atom displacing an electron and leaving a vacancy in a shell

2. Another electron de-excites to fill the shell releasing an X-Ray

Bohr model 5 limitations

• No proper account of quantum mechanics

• 2d model in 3d world

• For single-electron atoms

• predicted angular momenta too large by hbar

• no selection rules

Schrodinger - Free particle steps

1. Choose V(x)=0

2. Rearrange TISE for the second derivative

3. try particular solution: Ae^alphax

4. Find alpha=ik

5. sub psi into TISE

6. Find E=..

Schrodinger’s - Infinite Well

1. Outside box: psi(x)=0

   Inside box: V(x)=0

2. General solution: psi(x)=A sin(kx)+Bcos(kx)

   Boundary Conditions:

   1) x=0, psi = 0 → B=0

   2) x=L, psi = 0 and k=npi/L→ psi(x)=A sin(npix/L)

3. Total probability= 1:

   Integrate between 0 and L

   A=sqrt(2/L)

4. Psi = sqrt(2/L) sin (npix/L)

5. Energy = Substitute k=npi/L into energy for a free particle