PHYS1008: The end of Classical Physics

Objectives: by the end of this you will Understand how well all that we have discussed so far works Understand what went wrong

Summary of Classical Physics

• Haven't we learned a lot!

• Basis of Success: Newton's Laws of Motion valid for everyday objects, but also for very large
• Falling Apple ⇒ Planets ⇒ Galaxies
• and very small
• Conservation of Momentum & Energy ⇒ Kinetic Theory of gases
• Or Common Sense

  The layer of prejudices we acquire before we are sixteen" A. Einstein

• So what could go wrong?

Line Spectra

• Found black lines superimposed on sun's spectrum.

• Heated gases give characteristic wavelengths, and can match dark lines in solar spectrum to bright emission lines: e.g. Sodium

Hydrogen is simplest

• Balmer (1885) Found
• \color{red}{\frac{1}{\lambda } = R\left( {\frac{1}{{2^2 }} - \frac{1}{{n^2 }}} \right),R = 1.1 \times 10^7 m^{ - 1} } n = 3,4...
• Extends down into U.V., so only 4 lines can be seen easily.
• Subsequently Paschen found lines in the UV \color{red}{\frac{1}{\lambda } = R\left( {\frac{1}{{1^2 }} - \frac{1}{{n^2 }}} \right)}
• and Lyman found lines in the IR \color{red}{\frac{1}{\lambda } = R\left( {\frac{1}{{3^2 }} - \frac{1}{{n^2 }}} \right),}
• Problems
  • What gives the formulae?
  • Why do atoms only emit certain wavelengths?
  • How are absorption and emission related?

Photo Electric Effect

• Light falls on metal, ejects negative charge, which we now know consists of electrons: can measure energy of electrons by stopping them in an electric field

• No problem, since light carries energy?
• Problems for the PE effect:
  • The energy of electrons does NOT depend on intensity of light,
  • DOES depend on frequency.
  • No electrons emitted below critical frequency f₀, which depends on metal

Discovery of Electron

• J.J. Thomson's discovery of electron and measurement of e/m use velocity separator consisting of both mag. and E.S. fields:

• Electric Force FE = qE Magnetic Field into screen so force FM= Bqv

• For (3) Mag Field wins
• For (1) Electric Field wins
• For (2) no deflection so

  qE = Bqv  or v= E/B
  

• Allows e/m to be measured for an electron
• Millikan (1909) measured e
• charge of electron = -1.6 x 10^-19 C
• mass of electron = 9.1 x 10^-31 kg
• mass of H. atom = 1.67 10^-27 kg

• (Thomson): Currant bun model of atom,: electrons imbedded in positively charged material.

• Problems:
  • Why is the electron so much lighter than an atom?
  • What is the positive charge that must be in the atom?

Radioactivity Becquerel (1896)

• "Something" penetrating given off by certain materials (e.g. uranium salts). Subsequently saw that α- rays ~ helium nucleus β-rays ~ electrons γ-rays ~ X-rays

• Problems:
  • Where does the radioactivity come from?

Black-Body Radiation

• Black-body radiation: the radiation emitted by all hot bodies is (almost) exactly the same. Must measure temperature in degrees absolute (K).

  T(K) = T(oC) + 273
  

• so that room temperature (~20^oC) is ~ 300 K. For stars T ~ 6000 K ⇒ 20,000 K so doesn't matter whether we use K or ^oC!

  Two fundamental laws:

• Stefan-Boltzmann Total Energy \color{red}{U = \sigma T^4 ,\sigma = 5.67 \times 10^{ - 8} Jm^{ - 2} K^{ - 4} }
• Wien Wavelength of peak \color{red}{\lambda _{\max } = \frac{B}{T},B = 2.9 \times 10^ {- 3} mK^{ - 1} }
• What does this look like??

1. 1 W
2. 10 W
3. 100 W
4. 1000 W

• How much energy do you take in per day?
• You appear to radiate 10 times as much energy as you take in each day in food.

1. You actually wear clothes, and this stops the radiation.
2. Everything around you is at almost exactly the same temperature as you are, so it radiates back almost the same amount of energy.
3. You can't use conservation of energy in this way: in particular the energy you take in via food is quite different from the energy that you radiate.
4. This would be true at night, when there is no radiation hitting you from the sun.

• Note that this assumes that the body is a perfect radiator: a black-body.

• To derive a theory of Black body radiation put E.M. standing waves in cavity. no particular reason to assume that any one wavelength preferred to any other: short waves dominate (since there are more of them)

• this gives Rayleigh-Jeans curve. The "ultra-violet catastrophe": all radiation should be very short λ.

• Wien noticed that experimental curve looked like Maxwell-Boltzmann distribution. for molecules

• Problems:
  • Where does the B-B curve come from?
  • Why does it depend on temperature?

X-Rays

Röntgen (1895)

• Very penetrating radiation produced by vacuum tube (requires pot. diff ~ 20 kV), which passes through solids, fogs photographic plates

• First picture was of his wife's hand

Investigated by Moseley (1913)

After Röntgen, Moseley found that each atom gave characteristic X-rays

• Moseley measured

   E = 10.26(Z-1)² eV
  

  for most energetic X-Ray (K_α)
• First real measurement of atomic number. This formula looks a bit like the Balmer formula for hydrogen atom.
• Problem:
  • What are X-rays?
  • Where does Moseley's formula come from?

The Nucleus

Rutherford (1908) Lead block with radium salt: α-particles are produced by radium, collimated by screen to narrow beam, pass through gold foil and are detected by scintillator (produces spark of light when hit by charged particle

• Expect: rather small angle of deflection due to many small scatters

• Discover some deflected by more than 90^o
• How could this happen?

• Close encounter with electron? me ~ 1 mα 8000

• Cannonball bouncing backwards off tissue paper. Rutherford Need small, massive, positive charged nucleus. Electrons irrelevant!

• Why don't the electrons fall into nucleus?

• Maybe electrons are in orbit but an accelerating charge emits radiation so orbiting electrons should emit radiations and lose energy.

• Problems:
  • Why don't the electrons fall into nucleus?
  • Why are all atoms the same?

The End of Classical Physics

• Spectra Problems
  • What gives the formulae?
  • Why do atoms only emit certain wavelengths?
  • How are absorption and emission related?
• P-E effect Problems
  • The energy of electrons does NOT depend on intensity of light,
  • DOES depend on frequency.
  • No electrons emitted below critical frequency f₀, which depends on metal
• Thomson-Millikan Problems:
  • Why is the electron so much lighter than an atom?
  • What is the positive charge that must be in the atom?
• Radioactivity Problem:
  • Where does the radioactivity come from?
• Black Body Problems:
  • Where does the B-B curve come from?
  • Why does it depend on temperature?

• X-ray Problems:
  • What are X-rays?
  • Where does Moseley's formula come from?
• Rutherford's Problems:
  • Why don't the electrons fall into nucleus?
  • Why are all atoms the same?
• We would like an explanation of all of this!......