HUMS4100: The end of Classical Physics

Solar Spectrum: note the dark lines on the background.

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

• \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

• Millikan (1909) measured (indirectly) mass of electron = 9.1 x 10^-31 kg
• mass of H. atom = 1.67 10^-27 kg

• (Thomson) proposed 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:

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

• 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. and should not depend on temp. 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?

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X-Rays

Röntgen (1895)

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• 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
• Problem:
  • What are X-rays?

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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

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• 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!

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• 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?

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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
• Radioactivity Problems:
  • What is the positive charge that must be in the atom?
  • 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?
• 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!......