A group of particles move at many different velocities

The Quiz

• You are an astronaut floating in the vacuum of space, about 100 feet from the space shuttle. You are out there taking a picture of the Earth with your digital camera. When you are finished you realize that the jet pack you use to move around in space is no longer working. You are stranded and everyone is a sleep in the shuttle.

• What must you do in order to get back to the space shuttle? In explaining how you are going to get back describe how Newton’s three laws of motion will help you. All three are represented in this problem.

A balloon and the Sun

Magnetic lines of force trace out the magnetic field

Charged particles have similar force fields around them. In this case the fields are electric fields.

When a charged particle, such as an electron, is accelerated rapidly and for a very brief period of time, the distance field lines do not know that the electron has moved, while the close by field

lines point away from the charge like normal. The kink that is produced in the field is electromagnetic radiation (light). It moves

out away from the electron at the speed of light.

Imagine a charge being oscillated up and down rapidly. There are now a series of kinks produced in the electric field

A changing electric field produces a magnetic field. A changing magnetic field produces an electric field. In this way, the kink in the electric field, which is a change in the

electric field, produces a magnetic field. The resulting electromagnetic wave is self propagating.

The electromagnetic wave propagates out into space much like a water wave when a pebble is dropped in a

pond.

The wavelength of any wave (including EM waves) is the distance from one point on the wave to the next point where the pattern

repeats. For instance, the distance from crest-to-crest

What we perceive as color is just the wavelength of the EM wave.

Energy Conservation

• Energy can be neither created nor destroyed. • The total energy is always constant. Energy

just changes form.

• Potential Energy – Stored energy • Kinetic Energy – Energy of motion• Radiant Energy – Energy carried away by EM

wave

• ETotal = EPotential + EKinetic + ERadiant

Let’s summarize what we know.• Particles in a gas are in motion with a large range of velocities• The gas motion can be characterized by the average kinetic

energy of the gas. This is also how temperature is defined• When a charged particle is accelerated, a kink forms in the

surrounding electric field which propagates outward from the particle as a wave of electromagnetic (EM) radiation.

• The radiant energy in the EM wave is inversely proportional to the wavelength of the light. E = hc/λ

• Total energy is always conserved. It cannot be created or destroyed but only change type between Potential, Kinetic or Radiant.

In terms of energy conservation what must have happened?

1. The proton attracted the electron and changed its kinetic energy into potential energy

2. The electron’s kinetic energy was changed into radiant energy

3. When the electron slowed to nearly zero total energy dropped to almost zero

4. This can’t happen because kinetic energy is always conserved.

Which interaction produced the shortest wavelength of light?

1. Case A2. Case B3. Case C

The Sun is radiating.• The sun is radiating an enormous amount of energy

every second. ( Luminosity = 3.8 x 1026 watts)• This radiation is produced by moving, free electrons

that are interacting with other charged particles.• The particles are all constrained to be within the Sun

because the force of gravity from the Sun’s mass is pulling inward.

If this were all that is going on in the Sun;

What should we see happening to the Sun?

Please make your selection...

1. The Sun should be shrinking

2. The Sun should be expanding

3. The Sun should remain the same size

Our Sun is NOT shrinking

• The Sun’s particles are clearly converting their kinetic energy into radiant energy.

• In the process, the particles are losing kinetic energy. • This means that the average kinetic energy (or

temperature) should be decreasing with time.• IF the average kinetic energy decreases the particles

couldn’t hold up against the force of gravity. The Sun would shrink.

• Since it is not, we must conclude that some process is generating energy inside the Sun in order to re-invigorate the particles. (Answer: Thermonuclear fusion)

How can we measure the surface temperature of a star? (Note: temperature one of our stellar parameters)

• Measuring the average kinetic energy of a gas on Earth is easy. You do it every time you read a thermometer. But we can’t insert a thermometer in the Sun or the other stars.

• Energy conservation to the rescue. There is a direct connection between the kinetic energy of a gas and the radiant energy that the gas is producing.

A radiating source produces many colors of light.

• A radiating source may look red, or orange or yellow, BUT it is actually emitting light at many wavelengths. You can see this when the light is spread out into its components. Such as when water droplets spread light from the sun into a rainbow.

• This can also be accomplished with a prism or a diffraction grating.

A Spectrum

Top figure is the velocity

histogram for a gas.

Bottom figure is the

intensity verse wavelength

plot for stars.

The relation between particle kinetic energy and EM radiation

• If you have a very large number of fast moving electrons in a star then they will produce most of their light with high radiant energy, or short wavelength light.

• If you have a cooler star (more slowly moving electrons) they will produce mostly low radiant energy light, or long wavelength light.

• Result: cool stars look more red (long λ), hot stars look more blue (short λ) .

Wien’s Law gives us the temperature of the gas

• T = (2.9 x 106)/λpeak

• When light is spread out into a spectrum (a rainbow) it is possible to see which wavelength has the greatest intensity. (λpeak)

• The average kinetic energy of the particles in a gas is characterized by the peak in velocity histogram, the radiation curve shows us the peak in radiation, which comes from this average kinetic energy.

• The light from a star can be used to find the surface temperature.