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Modern Physics

Modern Physics. The Saga of Quantization. The Saga Begins…. Blackbody Radiation – radiation (electromagnetic waves) emitted by an object due to vibrating electrons. Emitted over a band of frequencies…but some frequencies are more intense than others. It Depended on Temperature.

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Modern Physics

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  1. Modern Physics The Saga of Quantization

  2. The Saga Begins… • Blackbody Radiation – radiation (electromagnetic waves) emitted by an object due to vibrating electrons. • Emitted over a band of frequencies…but some frequencies are more intense than others.

  3. It Depended on Temperature • The peak of the curve is in a different wavelength regions for different temperatures. • The peak could be predicted: lp T = 2.90 x 10-3 m K

  4. Exploring Wein’s Law • Look at the type of EM waves emitted UO Applet • What things do you notice? • P 782 # 6 lp T = 2.90 x 10-3 m K (18 x 10-9) T = 2.90 x 10-3 m K T = 1.61 x 105 K lp (2000 K) = 2.90 x 10-3 m K lp = 1.45 x 10-6 m = 1.45 mm

  5. The Shape of the Curve • But while the peak could be predicted, the rest of the curve could not be predicted using classical theory.

  6. Planck’s Hypothesis • Max Planck then said, well what if not EVERY value is allowed. • He realized that only integer multiples were allowed and the step size was constant: E = h f h = 6.626 x 10-34 J s (Planck’s Constant)

  7. What does it mean? • It means that energy actually comes in packets. • We cannot have any speed we want, only those that correspond to the energy steps. • We cannot have any frequency we want, only those that correspond to the energy steps. • Quantum mechanics was born.

  8. Why hadn’t we noticed it yet? • Big things are quantized, but if the step is small, then we do not notice the steps. • But when we get to small things, we start to notice the steps. • What things are small enough?

  9. Calculating Energy • All energy can be calculated for all wave properties as: E = h f (quantized energy) Example: Light at 5.15 x 1014 Hz E = 6.62 x 10-34 (5.15 x 1014) = 3.4 x 10-19 Joules

  10. Photons • But Joules per what? • Joules per photon! That means that light is both a wave and a particle. (We have heard this before…we see how we know this later on!) • If light is both a wave and a particle, then why can’t everything be a wave and a particle!

  11. Wave Particle Duality • Everything IS both a wave and a particle! • de Broglie then calculated the wavelength of any object: l = h / (mv) l = h / p (where p is momentum!)

  12. Your Car’s Wavelength • Let’s calculate your car’s wavelength on the freeway: l = 6.62 x 10-34 / (1000 kg * 25 m/s) = 2.6 x 10-38 m

  13. Let’s Try Something Smaller • Electrons have less mass and move faster… • = 6.62 x 10-34 / (9.11 x 10-31 * 1 x 105 m/s = 7.2 x 10-9 m = 7.2 nm Now that is something we can measure!

  14. The Diffraction of Electrons • Electrons have mass and are particles, but diffraction is a wave property!

  15. What about particles that don’t have mass? • l = h / (mv) • l = h / p (where p is momentum!) • Now we can calculate the momentum of a mass-less particle: • p = h / l

  16. Photon Momentum • What is the momentum of a photon of red light, wavelength = 650 nm? • We cannot calculate p = mv; we have the speed of light, but photons are mass-less! • l = h / p • 650 x 10-9 m = 6.62 x 10-34 / p • p = 1.01 x 10-27 kg m/s • This is why photons can be used to power space ships.

  17. Whiteboards • P 782 # 5, 37, 40, 44, 45

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