Module 12- Atomic and Particle Physics

Module 12- Atomic and Particle Physics

1. 12.1 Interaction of Matter with Radiation

   • Quantum nature of radiation
     • Max Planck and Albert Einstein spearheaded modern physics
     • Wien's Displacement law gives the relationship between wavelength and intensity for different temperatures
       • Wien's Displacement: Lambda max * T= 2.90x10^-3
       • Classical wave theory says thermal radiation is caused by electric charge acceleration near the surface of an object
       • For small wavelengths the actual values do not match with the predicted
     • Failing of classical theory was assuming energy could take any value
       • Planck hypothesised that if thermal oscillators only vibrate at specific frequencies delivering packets of energy he called quanta then the ultraviolet catastrophe was resolved
         • Planck's Hypothesis: En=nhf for n=1,2,3
         • Planck's Hypothesis- E=hc/lambda
       • Thermal oscillators can only absorb or emit light in chunks that are whole number multiples of E
   • Photoelectric Effect
     • Albert Einstein conducted experiments in which he irradiated photosensitive metals with light of different frequencies and intensities
     • Theorised that energy quantisation is also a fundamental property of electromagnetic waves
       • Called energy packets Photons and postulated that light acted like a particle as well as a wave
     • Certain metals are photosensitive which means that when they are struck with radiant energy they emit electrons from their surface
       • Light must have done work on the electrons
     • Einstein enhanced the photoelectric effect by placing a plate opposite and applying a potential difference, the positive plate attracts the photo-electrons and negative plate repels them
       • If he reversed the polarity of the plates, Einstein found he could adjust the voltage until the photocurrent stopped
     • Einstein found that if the intensity were increased, even though Ip increased substantially, the cutoff value remained V0
       • If the intensity is really low then photocurrent would still begin immediately
     • He also discovered that if the frequency increased, so did the cutoff value
       • If the frequency of the light was low enough then no matter how intense the light was, no photocurrent was observed. This is the minimum frequency needed to produce the photocurrent (cutoff frequency)
     • Einstein found that if he treated light as if it were a stream of particles instead of a wave then his theory worked
       • The light particle has the same energy as Planck's hypothesis photon
       • The work function is the minimum energy needed to knock an electron from the metal
         • Work Function = hf0
       • If the electron was freed by a proton having energy and if the energy was creater than the work function then the electron would have maximum kinetic energy
         • Maximum KE= EKMax= hf - work function= eV
     • Photoelectric Effect = hf = hf0 +eV
   • Wave Nature of Matter
     • A photon having a discrete packet and frequency is a statement of the wave-particle duality of light
     • de Broglie Hypothesis- Any particle having a momentum p will have a wave associated with it having a wavelength of h/p
       • de Broglie Hypothesis= h/p= h/mv
     • Diffraction of an electron beam matched de Broglie
   • Bohr Model of the Hydrogen Atom
     • Try to understand why Hydrogen had discrete energy levels
     • Hydrogen Radii= rn=n^2h^2/(4pi^2ke^2m)
     • Hydrogen Energy Levels= En=-13.6/n^2
   • Shrodinger Model of the Hydrogen Atom
     • He argued that since electrons must exhibit wavelike properties, in order to exist in a bound orbit, a whole number of the electron's wavelength must fit precisely in the circumference of that orbit to form a standing wave
     • Wave Equation= (Ek + Ep)Wave = E(Wave)
     • Wave Equation
       • Built around the conservation of mechanical energy
       • Wavefunction (Wave) which describes both the particle and the wave properties of matter simultaneously
       • The probability cloud shows where the electron has the highest probability of being
   • Tunnelling
     • We can imagine the particle to be trapped within a potential well
     • As long as an alpha particle's potential is less than change in V it appears that the alpha particle cannot get out of the nucleus
     • Inside the well, the particle oscillates as a standing wave, exactly like the electron in a box
     • Just outside, the waveform of the particle drops off exponentially. The bigger the mass the bigger the width of the barrier and the bigger the potential difference between the barrier wall and the trapped particle, the more rapid the exponential drop of the waveform
     • Outside, the waveform's exponential drop continues until it is infinitesimally small
     • The probability function tells us the probability of finding the particle at any position r
       • Probability Function= P(r)=Wave^2
       • The probability of finding a particle outside the potential well is extremely small but not 0
       • Radioactive decay is an alpha escaping
       • Barrier penetration is tunnelling
       • The smaller the charge and the smaller the mass, the easier it is for a particle to tunnel
   • Heisenberg Uncertainty Principle
     • Least intrusive observation is to bounce a photon off it and observe the results
       • Bounce a second photon off is velocity
       • Sending the two photons closer together gives the position and velocity to a degree of accuracy
     • It is impossible to know simultaneously an object's exact position and momentum
     • Momentum Form= Uncertainty in x* Uncertainty in p is greater than h/4 pi
     • Energy Form= Uncertainty in E* Uncertainty in t is greater than h/4 pi
     • The very act of observing its electron causes its momentum to change

2. 12.2 Nuclear Physics

   • Rutherford Scattering
     • J.J.Thomson discovered the electron and went on to propose a plum pudding model of the atom in which all the electrons were embedded in a spherical charge the size of the atom
       • Rutherford proposed that alpha particles would travel more or less straight without deflection if plum pudding was correct
     • Experiment on the structure of the atom by sending alpha particles through gold leaf
     • He proposed that all of the positive charge of the atom was located in the centre and he coined the term nucleus
   • Nuclear Radius
     • Nuclear Radius= 2Zke^2/R0. Where z is a value, R is a radius
     • Physical Radius of the nucleus also depends on its neutrons
       • Nuclear Radius=R=R0A^1/3
     • A nuclear radius can also be determined using collisions with alpha particles by measuring the diffraction of a beam of high energy electrons or neutrons having a de Broglie wavelength
       • Nuclear Scattering= Sin(theta)=lambda/D (slit width)
   • Radioactivity
     • Alpha particles are two protons and two neutrons
       • Alpha particles have an energy of 5MeV, energy needed to knock electrons off atoms is 10eV. One alpha particle can ionise a lot of atoms
       • Alpha particles are stopped by a few centimeters of air or a sheet of paper
     • Beta are electrons that come from the nucleus
       • Can have a large variety of kinetic energies. Neutrino postulated to carry extra KE
       • Stopped by a few millimeters of aluminium
     • Gamma Rays are photons and have no charge
       • Emitted when a nucleus de-excites
       • Gamma decay is evidence that the nucleus has energy levels
       • Very long distance
     • B- decay
       • A neutron becomes a proton and an electron is emitted from the nucleus
     • B+ decay
       • A proton becomes a neutron and a positron is emitted from the nucleus
   • Nuclear Stability
     • Stable isotopes exist for elements having atomic numbers 1 to 83
     • Up to z=20 the neutron proton ratio is close to 1
     • Beyond z=20 the neutron-proton ratio is bigger than 1 and grows with atomic number
     • Extra neutrons add to strong force without increasing repulsive force
   • Half Life
     • Unstable nucleus may spontaneously decay into another nucleus
     • The decay process is random
     • If there is a large enough population of an unstable nuclei, the probability that a certain proportion will decay in a certain time is well defined
     • Exponential decrease in decay rate
     • Half life is the time it takes half of the population of an unstable nuclide to decay
       • The higher the initial population of a radioactive material, the more decays there will be in a time interval
       • Law of radioactive decay= N= N0e^-lambda*t
     • We can measure the decay rate
       • Decay rates are measured using Geiger-Mueller counter
       • Decay rate are measured in Becquerels
         • (one Bq = 1 decay per second)
       • Activity Rate = -change in N/change in t= lamda n = lambda n0e^-lambda*t