Lecture: Blackbody Radiation

Exam

• Covers all material up to and including Friday, Sep. 22.
• A list of all but the simplest equations will be given.
• If constants, such as h and G, are needed, they will be provided. You should know the value of "c", the speed of light.
• An exam from last year is with the notes in Clark Library (covers slightly different material).
• You should know how to convert between meters, Angstroms and micrometers (microns).

Example equation list

Lecture Goals

• Learn some diagnostics associated with detecting radiation.
• Learn about blackbody emission.
• Learn about "21-cm" radiation.

Homework Problems

1. Photon A has l = 1000 A and photon B has l = 0.5 mm. Which carries more energy?
2. What does it means to say that energy levels in an atom are quantized? And what is the consequence?
3. Can a 9 eV photon ionize hydrogen?
4. A spectrum of a star peaks at 7250 A, what is its temperature?
5. If a star (a spherical blackbody) doubles in size and doubles in temperature, by what factor does its luminosity increase?

Emission from Solids

• Solid materials have a continuous spectrum rather than a discrete one.
• This is different from individual atoms.
• Examples:
  • Tungsten filament light bulb - continuous
  • Fluorescent lamp - discrete

Kirchhoff's Laws

• These are three laws that govern the spectrum we see from objects.
• They allows us to interpret the spectra we observe.

1. A hot solid, liquid or gas at high pressure has a continuous spectrum.

2. A gas at low pressure and high temperature will produce emission lines.

3. A gas at low pressure in front of a hot continuum causes absorption lines.

Heat Transfer

• All objects give off and receive energy.
  • In everyday life, we call this heat.
• The hotter an object, the more energy it will give off.
• An object hotter than its surroundings will give off more energy than it receives
  • With no internal heat (energy) source, it will cool down.

Energy Transfer

• Conduction:
  • particles share energy with neighbors
• Convection:
  • bulk mixing of particles, e.g. turbulence
• Radiation:
  • photons carry the energy

Internal energy of objects

• All objects have internal energy which is manifested by the microscopic motions of particles.
• There is a continuum of energy levels associated with these motion.
• If the object is in thermal equilibrium then it can be characterized by a single quantity, it's temperature.

Radiation from objects

• An object in thermal equilibrium emits energy at all wavelengths.
  • resulting in a continuous spectrum
    
• We call this thermal radiation.

Blackbody Radiation

• A black object or blackbody absorbs all light which hits it.
• This blackbody also emits thermal radiation. e.g. photons!
  • Like a glowing poker just out of the fire.
• The amount of energy emitted (per unit area) depends only on the temperature of the blackbody.

Planck's Radiation Law

• In 1900 Max Planck characterized the light coming from a blackbody.
• The equation that predicts the radiation of a blackbody at different temperatures is known as Planck's Law.

Properties of Blackbodies

• The peak emission from the blackbody moves to shorter wavelengths as the temperature increases (Wien's law).
  
• The hotter the blackbody the more energy emitted per unit area at all wavelengths.
  • bigger objects emit more radiation

Wien's law

• The wavelength of the maximum emission of a blackbody is given by:

  

Consequences of Wien's Law

• Hot objects look blue.
• Cold objects look red.
  
• Except for their surfaces, stars behaves as a blackbodies
  • blue stars are hotter, than red ones

Stefan-Boltzmann Law

• The radiated energy increases very rapidly with increasing temperature.
  
  

  
  
  

• When T doubles the power increases 16 times: 24 = 2x2x2x2 = 16

Energy Flux

• The Energy Flux, F, is the power per unit area radiated from an object.
  
  

  
  

• The units are energy, area and time.

Luminosity

• Total energy radiated from an object.
• For a sphere (like stars), the area is given by: Area = 4*pi*r^2 (m2)
• So the luminosity, L, is:

  

21-cm Radiation

• An important spectral line in astronomy for measuring the gas between stars is the 21-cm line of Hydrogen.
• This is in the radio part of the spectrum.
• The n = 1 level (ground state) of H is actually "split" into 2 levels separated by a very small energy.
• This splitting is due to the fact that the electron and proton have intrinsic spin, i.e. they behave like small magnets.
• When the North poles are aligned the energy is higher than when they are not.