Idea Transcript
Topic 13: Quantum Physics and Nuclear Physics Lessons: Photoelectric Effect and Einstein's Explanation Atomic Spectra, Wave Particle Duality and deBroglie's Hypothesis Shrodinger's model and the HUP The Nucleus Radioactive decay and questions (revision) Syllabus Statements: 13.1.1 13.1.2 13.1.3 13.1.4 13.1.5 13.1.6 13.1.7 13.1.8 13.1.9 13.1.10 13.1.11 13.1.12 13.1.13 13.2.1 13.2.2 13.2.3 13.2.4 13.2.5 13.2.6 13.2.7 13.2.8
Describe the photoelectric effect. Describe the concept of the photon, and use it to explain the photoelectric effect. Describe and explain an experiment to test the Einstein model. Solve problems involving the photoelectric effect. Describe the de Broglie hypothesis and the concept of matter waves. Outline an experiment to verify the de Broglie hypothesis. Solve problems involving matter waves. Outline a laboratory procedure for producing and observing atomic spectra. Explain how atomic spectra provide evidence for the quantization of energy in atoms. Calculate wavelengths of spectral lines from energy level differences and vice versa. Explain the origin of atomic energy levels in terms of the “electron in a box” model. Outline the Schrödinger model of the hydrogen atom. Outline the Heisenberg uncertainty principle with regard to position–momentum and time–energy. Explain how the radii of nuclei may be estimated from charged particle scattering experiments. Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer. Describe one piece of evidence for the existence of nuclear energy levels. Describe ß+ decay, including the existence of the neutrino. State the radioactive decay law as an exponential function and define the decay constant. Derive the relationship between decay constant and half-life. Outline methods for measuring the half-life of an isotope. Solve problems involving radioactive half-life.
The Photoelectric Effect and Einstein's Explanation A photon is a pulse of electromagnetic radiation. It is created when an electron in an atom releases energy. Electrons in Atoms: We know that electrons orbit the nucleus of an atom. The distance an electron is orbiting from the nucleus depends on the energy that it has. For example an electron with lots of energy will orbit further from the nucleus than an electron with little energy. By analogy a satellite orbiting a long way from the earth will have more GPE than a satellite orbiting close to the earth. BUT Unlike the satellite analogy electrons cannot orbit the nucleus at any distance. They must be in one of a set of discrete (definite) orbits. Each one of these orbits has a particular energy associated with it. The energy an electron must have to be in that orbit. No more, no less. Hence these orbits are called energy levels. Diagram of energy levels in an atom.
It follows therefore that if an electron wants to change the orbit that it is in, then it must gain or lose energy, and the amount of energy depends on the two orbits that it is moving between. In making this transition the electron must emit or absorb an exact amount of energy - a photon. Because atoms only have discrete energy levels, a photon can only have discrete values of energy. Energy level diagram showing possible transitions between energy levels and thus possible photon energies.
The energy that a photon has can be measured from the frequency of its radiation by. E = hf This can also be related to the wavelength of the radiation by. c = f l so f = c/ l so E = hc/ l Task: Consolidate this by working through the 3 online pages from University of Colorado. Question: What is the energy range in eV, of photons in the visible spectrum, of wavelength 400 nm to 700nm? What is the energy of photons (in eV) emitted by a 102.1MHz FM radio station? The Photoelectric Effect If we charge up a zinc plate and connect it to a gold leaf electroscope we observe the level of charge qualitatively from the repulsion of the gold leaf. If light from a mercury lamp is then shone on to the zinc plate, it discharges.
Why? Somehow the light is helping the electrons to escape. If we move the lamp closer the intensity increases and the plate discharges faster, but... If a piece of glass, which absorbs UV light, is placed between the lamp and the plate, then it no longer discharges. Conclusion... It must be that the UV light is the only frequency that is effective at discharging the plate. Task: Work through the online photoelectric effect simulation. Write up your findings for your notes. The light must have a frequency of UV or above to release electrons from the zinc plate. The minimum frequency of light that will do this is called the Threshold Frequency. Einstein's Explanation This stumped physicists for quite a while until Einstein came along. The video explains how Einstein solved the problem. The complete lecture is well worth going through and revises some concepts we have met before. Photons eject electrons from the surface of the charged metal...
hf = f + E max , so... hf = f + ½mv 2, where... f is the work function. The minimum energy of a photon required to eject an electron from the metal. f = hf o where f o is the threshold frequency, the minimum frequency of a photon required to eject an electron from the metal. NB: different metals have different threshold frequencies and hence work functions. Task: Write a set of notes to explain how Einstein explained the photoelectric effect, and how he used the concpets of work function and threshold frequency to achieve this. A nice poster charting the development of the theory. Exercise: Complete the online exercise to detemine Plank's constant, the work function and the threshold frequency of three different metals. Questions: Topic 13 teaching questions 2-13 A very good video clip to underpin all of this, and demonstrate important applications of the photoelectric effect (and some awesome hair styles!) Hutchings pp521-525, Kirk and Hodgeson pp207-209. Back to topic 13 Atomic Spectra, Wave-Particle Duality and deBroglie's Hypothesis Spectral lines show us the absorption and emission of photons associated with energy levels of a particular atom. Because different atoms have different energy level arrangements the energies and therefore frequencies (E=hf) and therefore wavelengths ( l =c/f) associated with these photons are specific to that atom. Emission spectra for different elements Bohr's step was to say that for this to be possible electrons can only exist in certain energy levels within the atom. If this wasn't true then an atom would be able to absorb and emit any energy (therefore frequency, therefore wavelength) photon, and this is not observed. deBroglie explained this further by considering wave particle duality of electrons. Einstein had already shown that photonss can behave as particles as well as waves, so why couldn't electrons behave as waves as well as particles? If a particle is to behave like a wavethen it must have a wavelength asociated with it... The energy of a photon is given by E = hf, The mass (equivilence) of this energy is given by E = mc 2 Equating the terms gives... hf = mc 2 hc/l = mc 2 h/l = mc This is the momentum of a photon, but for ordinary matter not moving at the speed of light.. h/l = mv thus the deBroglie wavelength is given by... l deBroglie = h/mv So what is your deBroglie wavelength? deBroglie went further though and sugested that this explained the Bohr theory: that electrons could only occupy certain energy levels because they must exist in an orbit around the nucleus which has a circumference equal to a whole number of wavelengths. Applet to demonstrate Tasks: 1. Work through the simulation to get a working understanding of Bragg's law. 2. Find out the details of the Davisson-Germer experiment to verify deBroglies hypothesis.Ref: http://hyperphysics.phyastr.gsu.edu/Hbase/quantum/davger2.html. 3. Now repeat the experiment for yourself using this applet to record and analyse your data to demonstrate deBroglie's theory l deBroglie = h/mv. 4. Write a page to explain what they did and what it proved. Questions: Topic 13 Teaching Questions 14-17 Hutchings pp525-527, 530-531, Kirk and Hodgeson pp209-210. Back to topic 13 Shrodinger's Model and the Heisenburg Uncertainty Principle With the electrons now behaving like waves, Schrodinger re-thought the model of the atom. Based on deBroglie's hypothesis that the electrons associated with a particular atom must occuply energy levels that constitute whole numbers of wavelengths, that electrons are not infact particles, but standing waves that do not transfer energy. Schrodinger developed this idea by suggesting that if electrons are not particles, then the charge that they carry must be distributed over an area. He developed a model whereby he could determine the probability of finding the charge of an electron at a particular location in the allowed orbit of the electron. The applet helps you to visualise this idea, by developing it in the stages of development we have considered. Schrodinger suggested that each electron could be described by a mathematical equation called its wavefunction. You can basically think of this as being the equation of the wave that fits its orbit. If we consider the 'electron in a box model' this is easily explained. An electron can have one of several different wavefunctions to describe itself as a standing wave in an orbit of a given length (represented by the box). The different wavefunctions effectively show the different harmonics of the possible standing waves. Applet to explain this The square of the wave function gives the probability of finding the electrons charge in a particular place in the orbit. Task: Complete the worksheet which works through the idea Schrodinger developed as applied to the Hydrogen atom. The Heisenburg Uncertainty Principle Werner Heisenburg developed his, similar, theory at about the same time as Schrodinger. They were later found to agree, although the mathematics that demonstrates this is very tricky. Heisenburg said that there is an intrinsic uncertainty in any two measurements of position and momentum of an object. It is not possible to accurately know both of these quantities for an object (conjugate quantities), indeed by knowing one you are effectively lose the ability to know the other. The uncertaintainties in these values are related to each other...
. Another way of expressing this is using a particle's energy and time...
. These theories essentially mean that the universe is indeterministic- In other words similar causes lead to different effects. This in sharp contrast to classical physics which is deterministic (the future is uniquely determined by the present plus the laws of physics). Quantum physics is indeterministic (the future is not completely determined by the present plus the laws of physics – it remains open). Einstein hated these ideas, thinking that Physics could surely not be a game of chance, "I am convinced that he (God) does not throw dice". However the more experiments we do to investigate the world of the very small, the more evidence we gain that Quantum Mechanics is correct, and the universe is indeterministic! Indeed does free will not require this to be the case? Feynman's explanation of this. An excellent precee of Heisenburg So what have we learned about the atom? Questions: Topic 13 Teaching Questions 18 Kirk and Hodgeson pp211-212, 216-217. Back to topic 13 The Nucleus Considering that it is too small to see, we know quite a lot about the nucleus of atoms. We have had to be quite inventive though to find things out. How big is it? Thinking again about Geiger and Marsden's experiment, scattering alpha particles off gold nuclei, a rudimentary estimate of nuclear size can be determined by considering the proportion of alpha particles that are scattered. This must be the same as the proportion of atomic volume occupied by the nucleus. Thinking more carefully, we realise that looking at the kinetic energy of 180o back scattered alpha particles provided us with the most compelling estimate of nuclear size. Knowing the kinetic energy of an incident alpha particle (which we can control, by accelerating it across a controlled voltage), and equating it with electrostatic potential, gives us the ability to determine, r, the distance of closest approach...
The higher the energy of the incident alpha particle, the closer it will get to the nucleus. We know that it hasn't got to the nucleus, because no nnuclear reaction is seen to occur, and occasional back scattered alpha particles are still observed. Therefore the higher the energy of the incident alpha, the closer we get to determining the radius of the nucleus. Applet to demonstrate Task: Work through and answer the questions on Rutherford scattering: Energy and closest approach How heavy is it? (What is its mass?) We can determine nuclear mass by considering the effect that a force has on it. Remember that our definition of mass is in terms of its inertia (the bigger the mass, the smaller a force's effect), m=F/a. 1. A particle (nucleus) of known charge is accelerated through a known EMF, thus its energy is known by E=qV. 2. The particle is passed through a velocity selector, such that its velocity is known. This works by applying perpendicular electric and magnetic fields, also perpendicular to the particle's velocity. By controlling the strength of the B and E fields, only particles of a certain velocity can continue undeflected.
3. If we now send the charged particle into a known magnetic field, then we know it will be deflected by the part of the magnetic field perpendicular to its motion. The deflection is a curved path, suggesting the presence of a centripetal force, which must be supplied by the magnetic force acting on it...
Since we know the charge of the particle, and the velocity at which it is moving, we can therefore determine its mass by measuring the radius of curvature it experiences when travelling through a known magnetic field. This is the principle of operation of the Bainbridge mass spectrometer Task: Work you through this nice online experiment to further your understanding of this. Questions: Topic 13 Teaching Questions 19-23 Kirk Revision Guide pp109 Back to topic 13 Radioactive Decay We think the nucleus has discrete energy levels in the same way that electrons do. We have come to this conclusion based on evidence similar to that underpinning our electron energy level model. Just as electrons emit photons of discrete energies (defined by their observed wavelengths), nuclei are seen to emit particles of discrete energies. A graph plotting kinetic energies of emitted alpha particles shows this pattern. Alpha Particle Energy Spectrum
We also see a pattern like this for emitted gamma particles, but not for beta particles. Why not? Question: What is the difference between beta emission, and alpha and gamma emission? (Hint: consider the equations you learnt in year 12) The answer is the neutrino. In beta plus and beta minus decay, a neutrino is also emitted. This was predicted initially to explain why beta particles could have a continuous spectrum when it was known that nuclei had a quantised system of energy levels. Beta Particle Energy Spectrum
By predicting the existance of another particle, Physicists could explain the continuous spectrum of beta particles by saying that the rest of the energy from a nuclear transformation is carried away by the neutrino. This would mean that neutrinos would have a continuous energy spectrum too. Observation of this is extremely difficult, as neutrinos are very hard to observe, since they are highly uninteractive. But we have done it! The remainder of this topic is simply revision of topic 7. Modes of nuclear decay (alpha, beta (+/-/electron capture), and gamma) The quantities of decay constant and half life and the relationship between them. Task: Revise these concepts to help you answer the following questions... Questions: Topic 13 Teaching Questions 24-31 Kirk Revision Guide pp109-110 Back to topic 13
anrophysics 2007