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Modern Physics

This overview of modern physics delves into the fundamental concepts of quantization, beginning with blackbody radiation emitted by vibrating electrons. It discusses the dependence of intensity on frequency and temperature, introduces Wien’s Law, and elaborates on Planck’s Hypothesis regarding energy quantization. The text explores how energy comes in discrete packets, leading to the birth of quantum mechanics. It also covers wave-particle duality and illustrates calculations for the wavelengths of objects, including everyday examples like cars and electrons, showcasing the interplay between mass and wave properties.

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Modern Physics

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Presentation Transcript

  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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