Black Body Radiation

Question 1

What does it mean if an object (not a star) is red?

Answer 1

Absorbs all light except red photons, which it reflects.

Question 2

Why is a star like Betelgeuse red?

Answer 2

Emits red photons.

Question 3

What is a black body?

Answer 3

A perfect absorber/emitter, absorbs all intercepted photons.

Question 4

What emits EM radiation?

Answer 4

All objects with T > 0K

Question 5

What is thermal equilibrium?

Answer 5

The matter and radiation field have the same temperature.

Question 6

What do typical black body curves look like for different temperatures (intensity plotted against wavelength)?

Answer 6

High temperature looks like negative skewed graph, and gets lower with the peak further to the middle as temperature decreases.

Question 7

What is the equation for black body intensity at λ as a function of T?

Answer 7

B(T) = 2hc^2/λ^2 * 1/(exp(hc/λkT)-1)

Question 8

What is the equation for the quantisation of energy?

Answer 8

E = hc/λ

Question 9

What is the first property of the Planck function?

Answer 9

Area under the black body curve gets larger as you move to higher temperatures.

Question 10

What is the equation for radiance?

Answer 10

integral from 0 to inf of B(T) dλ = σT^4/π

Question 11

What is the definition of radiance?

Answer 11

Total energy radiated per unit surface area of a black body across all wavelengths per unit time per steradian.

Question 12

What is the second property of the Planck function?

Answer 12

The black body peak wavelength moves bluer with temperature.

Question 13

What is Wiens law?

Answer 13

λmax*T = const

or

log λ = -log T + C

Question 14

What does the log black body curves graph look like?

Answer 14

Lines going up and then turning and going down, moving higher and to the left with temperature.

Question 15

What is a solid angle?

Answer 15

3D analogue of an angle. Units are steradians.

Question 16

What do we need to compute to relate intensity and flux?

Answer 16

Triple integral over all angles to get total intensity (luminosity)

Question 17

What is the equation for luminosity in terms of black body intensity?

Answer 17

L = 4πR^2πB(T) = 4πR^2*σT^4

Question 18

How do we relate the black body intensity with flux?

Answer 18

Use the two luminosity equations and set them equal to each other.

Question 19

What is the integral equation for the black body intensity?

Answer 19

B(T) = integral from 0 to inf of B(T) dλ

Question 20

What is the effective temperature and what is its equation?

Answer 20

The temperature that the star would have if it were a black body. F = σTeff^4

Question 21

How many temperatures are there for which a blackbody emits the same amount of energy as the star? What does this imply?

Answer 21

One temperature, implying that black body curves do not cross eachother at all, hence black body curve has a unique temperature.

Question 22

Give an example of a black body radiator.

Answer 22

A cavity radiator (heatable cavity with small aperture).