Four Chapter 9

Heisenberg's Uncertainty Principle

• Particles behaving as waves and waves behaving as particles results in a need to look at events in a new way
• So far, calculations show that even electrons can be delt with in precise ways.
• Heisenberg in 1927 suggested that there is always some uncertainty in determining exact positions and speeds (energies) for electrons
• The uncertainty was due to the quantum mechanical nature of subatomic particles.
• Suppose we try to determine the position of an electron in an atom.
  • To determine position, we must irradiate the electron with light in order to see the electron.
  • Momentum of a Photon is

P = h/ l

• With light, we can locate things only to the accuracy equal to about the wavelength of light.
• Since electrons are very small, we must therefore use a very small wavelength of light to locate the electron.
• If the wavelength is small, then frequency is large (C = f l), and momentum (P = h/ l) is large.
• The energy of the photon (E = hf) is therefore also large.
• high energy, high momentum photons, when they contact an electron, will transfer significant momentum and energy to the electron
• As a result, we can locate were the electron was, but not know its new momentum or energy.
• The smaller the wavelength is, the larger the momentum and energy is for the photon. Therefore, we know accurately the location, but not momentum, since the momentum will be severely affected.
• If we use a larger wavelength so that momentum is smaller (P = h/l) and energy is smaller
• (E = (hc)/l), then the momentum of the electron is less affected (we know it more accurately), but we don't know the position as well.
• As a result of this, Heisenberg stated his Heisenberg uncertainty principle
  • Heisenberg uncertainty principle - We are unable to know the position and momentum of an electron with unlimited accuracy.

DX DP ³ h/(2p)

DE DT ³ h/(2p)

DP = mDv

• In these equations Dv = uncertainty in velocity, DP = uncertainty in momentum, DE = uncertainty in energy, DT = uncertainty in time interval, and DX = uncertainty in position.
• The equation DE DT³ h/(2p) tells us that the smaller the time interval, the greater the uncertainty in energy.
• Uncertainty is unimportant for large size objects.
  • Consider a 1 kg object with momentum P = mv.

• Therefore, for large objects, uncertainty is not very significant.
• Uncertainty is significant for small objects.

• This uncertainty is significant.
• The uncertainty in location for the electron makes it impossible for us to prove that electrons are moving in well defined orbits by direct observation.
• This means that Bohr's theory cannot be varified by direct observation
• We therefore need a new look at the atom

Probability and Determinism

• Newton viewed the universe as deterministic.
• Given the present motion, location, etc, the future location etc, for a particle could be determined.
• Bohr held this view with respect to the atom.
• Because of the uncertainty in knowing position and momentum of an electron, it becomes impossible to say where the electron is now, and where it will be in the future.
• We must satisfy ourselves with describing the probability of finding the electron near any point.
• Because of its wave properties, the electron in an atom cannot be visualized as a particle.
• It must be visualized as being a wave spread over the entire atom.
• The amplitude of the de Broglie wave represents the probability of finding the electron at a specific postion.
  • For the first Bohr orbit, the highest probability (highest amplitude) occurs in a spherical shell of radius 5.3 X 10^-11 m.
  • The amplitude is non-qero else where, but is smaller, therefore the probability elsewhere is non-zero.
  • The shapes of the other Bohr orbits are different.
• In 1925, Heisenberg and Schrodinger independently developed equivalent mathematical equations. the solutions of these equations give the probability distributions for virtually any problem in quantum mechanics.
• The equation became known as the Schrodinger equation.
• The equation does the following
  • gives solutions to atomic structure problems
  • provides mathematical interpretations of physical situations
  • gives values for measurable quantities such as
    • momentum
    • energy
    • probability for all possible locations of particles

Radioactivity

• Our understanding of wave particle duality led to an understanding of why some atoms are radio active and others are not.
• Particles in the nucleus of radioactive atoms are able to penetrate through the barrier which holds them there. This barrier is caused by the strong nuclear force.
• The investigation of radioactivity began with studying fluorescence, in which some materials radiate light at a different wavelength than the light they absorb.
• This fluorescence occurs when most of these materials are exposed to
  • cathode rays
  • X-rays
  • light.
• Early investigators thought that x-rays may be produced by fluorescing materials.
• To test this idea, Becquerel placed crystals known to fluoresce in sun light on top of photographic plates wrapped in black paper. While experimenting, Becquerel placed a compound containing uranium on a photographic plate. Because it was cloudy, he didn't perform the experiment. instead he put it aside. He discovered that the photographic plate was exposed even though it was not exposed to sun light.
• Becquerel concluded that uranium emits radiation without being exposed to sunlight. Becquerel had discovered radioactivity.
• Other radioactive materials were sought and also an explanation for radioactivity was needed.
• Marie Curie found that the amount of radiation depended only on the amount of uranium present and not on any other factor.
• This suggested that radioactivity is determined by something inside atoms.
• Curie examined the ores from which uranium is obtained.
  • She found the ores were more radioactive than uranium.
  • This suggested to her, that other more radioactive substances exist.
• She ground up pitchblende (20 kg) , dissolved it, filtered it, crystallized it, collected it, re-dissolved it etc, over and over again. As a result, she discovered an element 300X more radioactive than uranium. She named it polonium.
• Curie and her husband noticed that the residue from this process was also very radioactive (900X more radioactive than uranium).
• They isolated another element from the residue and called it radium.
• Radium was soon found to be useful in the treatment of cancer (kills the cells).
• At the same time, the hazards of radiation were becoming apparent. The Curies complained about continuous fatigue and poor health, but refused to believe that radiation could have long term effects.
• Marie Curie died with all the symptoms of radiation sickness. In the 20 years following Curie's experiments, more than 100 people died from exposure to radioactive elements and their radiation.
• Curie and Becquerel noticed that some of the radiation could be deflected by magnetic fields. One part deflected as if it were a negatively charged particle. Another part deflected as if it was a positively charged particle.
• Pierre Villard discovered a third and more penetrating radiation that was unaffected by magnetic or electric fields.
• In 1889, Rutherford, working at McGill, named the three radiations.
  • Alpha particles (a)
  • Beta particles (b)
  • Gamma rays (g)
• Rutherford placed a small bit of radium in a lead box with a hole at one end. This produced a narrow beam of radiation upon which Rutherford performed experiments.
• Rutherford and others discovered the properties of alpha, beta and gamma radiation.
• ALPHA PARTICLES
  • They are positively charged particles (nuclei of helium atoms).
  • They are ejected at high speed but have a range of only a few centimeters in air.
  • They are stopped by an ordinary sheet of thin aluminum foil.
• BETA PARTICLES
  • They are streams of high energy electrons.
  • They are ejected at various speeds, sometimes approaching the speed of light.
  • Some particles are able to penetrate several millimeters of aluminum.
• GAMMA RAYS
  • They are electromagnetic radiation with very short wavelengths.
  • Their wavelengths and energies can vary.
  • High-energy gamma rays can penetrate at least 30 cm of lead or 2 km of air.
• IONIZING RADIATION - Alpha, beta and gamma radiation.
• All three types of radiation can ionize nearby atoms and molecules.

Radioactivey Detectors

• The earliest detectors of radiation are
  • photographic film
  • fluorescent substances
• Later detectors used the fact that radioactive emissions tend to ionize atoms and molecules.

Geiger - Muller Tube

• Consists of
  • Large cylindrical cathode
  • Wire (anode) down the center
  • The tube is filled with argon gas at low pressure and a trace of bromine.
  • Thin mica window at one end.
• A high energy particle enering the tube ionizes the gas. The ions are attracted to the electrodes
• As the ions move to the electrodes, they ionize other atoms.
• As a result, a small current inside the tube is set up.
• The current produces a click or causes a counter to increase by one.
• Each click indicates one particle
• Used to count alpha and beta particles.
• The disadvantage of the tube is that it requires a recovery time between particles of about 100 micro seconds. As a result, if the numbers of particles are too high, it won't count them all.

Cloud Chamber

• Cloud chambers are a container which is supersaturated with alcohol vapour or water vapour.
• Charged particles travelling through the chamber knock electric charges off of the air
• molecules they hit.
• These particles attract nearby vapour molecules and cause the formation of tiny visible drops
• The result is a vapour trail through the chamber.
• The appearance of the tracks is different for different particles.

Scintillation Detector

• Alpha particles striking a thin layer of zinc sulphide causes a flash of light (scintillation) at the point of contact.

Bubble Chamber

• Uses liquid (usually liquid hydrogen) kept near the boiling point.
• When particles move through, they lose energy to the liquid and this results in vaporization of the liquid along the path (bubbles form).
• Strong magnetic fields cause fhe particles to move in curved paths.
• The direction of the curve tells you the charge on the particle.
• Radius of the curve tells us about the mass and speed of the particles.

Spinthariscope

• By mounting a zinc sulfide screen and looking at it through a magnifier, alpha particles could be detected.
• Not used much, but was used in investigation of the structure of the atom.
• Modern counters use electronic means to convert flashes of light into measurable electric current.

Photomultiplier

• A phosphorescent material is cemented to a photo cathode which when light falls onto it, the material emits an electron.
• Therefore for every particle entering the phosphorescent material, an electron is emitted from the photo-cathode.
• This electron is accelerated towards the first of many positive electrodes (called dynodes)
• When it strikes the dynode, it causes two to five electrons to be emitted from the dynode. This occurs due to the energy gained by the electron during acceleration.
• This process continues down the photomultiplier tube. The multiplied signal is sent to a counter, which counts the number of particles entering the phosphor
• It is good for alpha, beta and gamma radiation.

Semi Conductor Devices

• When an electric potential difference is placed across the device, then a particle passing through the material causes ionization which briefly modifies the electrical characteristics of the device.
• The resulting electrical pulse can be counted as in other devices

Smoke Detectors

• There are two types
  • photoelectric
  • ionization
• Photoelectric - light passes through a chamber onto a photocell. Smoke in the chamber reduces the intensity of light and therefore current which sets off the alarm.
• Ionization - a radioactive source (usually americanium), emits alpha particles which ionizes nitrogen and oxygen molecules in a chamber.
  • This ionization results in a small current in the chamber.
  • Smoke, when present, is attracted to the ions and this discharges the ions. This results in reduced current which set off the alarm
• Some Detectors are a combination of the two.

Units of Radioactivity

• becquerel (Bq) - unit used to measure radioactivity

1 Bq = 1 emission/second

January 22, 2014