Particle Nature of Matter. Chapter 4

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1 Particle Nature of Matter Chapter 4

2 Modern physics When my grandfather was born, atoms were just an idea. That year, 1897, was marked by the discovery of the electron by J.J. Thomson. The nuclear model was established by Rutherford, Geiger and Marsden in And in that year, Bohr produced the first quantum model of the atom.

3 Atomic physics Chemistry suggests the idea of elemental substances Complications: Masses of most common isotopes are not quite proportional to atomic number. Isotopes: Fixed atomic number can have different mass Alloys, mixtures

4 Electrical nature of atoms The polar nature of water molecules dissociates salts. Ion curent reveals a relationship between charge and mass in chemical reactions.

5 Electrical nature of atoms In electrolysis of NaCl, 96,500 C of charge passes while 23 gm of Na is deposited and 35.5 gm of Cl gas formed. Why? Formation of ions with quantized charge.

6 Cathode rays Cathode rays were discovered as emissions from negatively charged metal elements.

7 Thomson s experiments Electrons from the cathode are accelerated through anode slits and deflected with electric and magnetic fields.

8 Charge to mass ratio For an electric or a magnetic force, the acceleration and deflection are proportional to q/m - neither q nor m is determined independently. An independent measurement of the electron charge would permit derivation of the electron mass. => Millikan s oil drop experiment.

9 Speed of electron in CRTs For accelerating potential V~ kv, the axial velocity is given by (nonrelativistic) energy conservation 1/2 mv^2=qv=>v=[2qv/m]^1/2 Work it out - the speed is fast but 1 kev<<511 kev so v<<c. Thomson did not have the means to measure the travel time.

10 Millikan s experiment Observe singly charged microscopic drops levitated by an electric field. Force balance mg =qe gives charge as q=mg/e

11 Millikan s experiment What radius drop with net charge e can be suspended between two plates of separation h= 1 cm and voltage V?

12 Millikan s experiment What radius drop with net charge e can be suspended between two plates of separation h= 1 cm and voltage V?

13 Conclusions The charge to mass ratio q/m and the charge e give the electron mass Gulp: Electrons determine electrical/chemical properties of elements BUT the mass of an atom is not electronic!

14 Quark searches In the 1970s, particle physics was focused on fractionally charged quarks - d -1/3 an u +2/3. The proton composition is p=uud. The neutron compositions is n = udd. The Millikan experiment was repeated with laser jet printing technology. No fractionally charged drops were found. Quarks are confined by incredibly strong color forces into color neutral composites. Free quarks were not observed.

15 Rutherford scattering Radioactivity provides high energy particles capable of probing the atomic nucleus. An alpha particle emitted in nuclear decay has kinetic energy of several MeV typical of nuclear energy scales.

16 Rutherford scattering Rutherford, Geiger, Marsden studied alpha scattering from thin foils of metal.

17 Nuclear scattering model Most likely is a collision with large impact parameter/distance from nucleus, and with small scattering angle. Large angle deflection results from a more rare collision in which the alpha gets near to the nucleus.

18 Details of angular dependence Theory: Calculate trajectory and deflection at given impact distance. Multiply by probability of hitting an annulus of that distance. It works! Small deflection large deflection

19 Conclusion The mass of an atom is concentrated in a positively charged atomic nucleus. The nuclear radius is roughly 10,000 times smaller than the atomic radius.

20 Problem with model Imagine a solar model - light negatively charged electrons orbiting a heavy positively charged nucleus. The Coulomb force is proportional to 1/r 2 just like the gravitational force so the orbits are ellipses. The electrons are accelerated so will radiate EM waves, lose energy, spiral in towards the nucleus. The time to spiral from ~10-10 m to m may be calculated to be of order 1 ns. Atoms should collapse!! What stabilizes the atom?

21 Questions of physics Some questions are so simple to state! What is the sky dark at night? Why is it cold in the winter time? Why does matter not collapse (forming a black hole)? What is light? What is matter for that matter? Why are things the size they are?

22 Stability of matter Newtonian/Maxwellian physics predicts collapse. Something keeps this from happening. (Quantum mechanics)

23 What light do atoms emit? A prism may be used to separate the frequencies in a mixture of light.

24 Atomic emission spectra Atoms do radiate light, but the spectrum is not continuous. Each element emits a characteristic spectrum of discrete frequencies which tell us something about the electrons within.

25 Absorption spectra (Sun) Atoms absorb radiation at the same frequencies at which they emit. From signature spectra, one can deduce the kinds of atoms in a source like the Sun!

26 Hydrogen Hydrogen is the simplest atom - just one electron orbiting a single proton. It should hold the key to atomic physics.

27 Rydberg s formula The discrete wavelengths emitted or absorbed by hydrogen fit a simple formula: The subscripts I and f as we will see refer to initial and final states of the electron.

28 Spectral series For a fixed final state, a series of wavelengths is historically associated with a different investigator.

29 Bohr s model F=ma permits circular orbit at any radius. Guess angular momentum quantization - only discrete radii allowed.

30 In this picture only certain orbits are permitted. Bohr model radii The minimum radius (n=1) is called the Bohr radius. This condition is called the ground state.

31 Bohr model energies Given the radius we can find the kinetic energy Given the radius we can find the potential energy The total energy for a given n is

32 Bohr model energies Transitions between states implies emitted energy spectrum just as observed:

33 Example Bohr model energies What wavelength will excite monatomic hydrogen from the ground state (n=1) to the n=3 state?

34 Example Bohr model energies What wavelength will excite (monatomic) hydrogen from the ground state (n=1) to the n=3 state?

35 Franck-Hertz experiment Photons are emitted when an electron in an excited state transitions to a state of lower energy. Photons are absorbed and excite electrons from lower energy to higher energy states. Collisions can also produce quantum excitation.

36 Franck-Hertz experiment Bombard gaseous atoms with electrons.

37 Franck-Hertz experiment Current vs accelerating voltage

38 Franck-Hertz experiment When electron energy is sufficient to excite an atom, accelerated electron transfers energy to the atom, comes to rest and proceeds onward. A stripe of gas is excited and florescence light is seen.

39 Reduced mass effects In classical physics, two bodies orbit the center of mass. The solution is equivalent to that of one object orbiting a fixed point but with a reduced mass. Careful measurement reveals R should be calculated with the reduced mass for electron and proton.

40 Check on Bohr model In deuterium, the nucleus is p=>pn and about twice as heavy slightly changing. In He+, the nucleus is ppnn and we need e 2 => Ze 2 =2e 2 and a different reduced mass. We learn Bohr s model works for other hydrogen like cases - he is on to something. But what??

Chapter 28. Atomic Physics

Chapter 28. Atomic Physics Chapter 28 Atomic Physics Sir Joseph John Thomson J. J. Thomson 1856-1940 Discovered the electron Did extensive work with cathode ray deflections 1906 Nobel Prize for discovery of electron Early Models