Stars & EA 4

Question 1

What 2 types of properties do stars have and how are they connected?

Answer 1

Stars have physical and observable properties. We must use the observable properties to find the physical properties.

Question 2

List some physical properties.

Answer 2

Luminosity
Absolute magnitude
Size
Mass
Temperature
Velocity

Question 3

List some observable properties.

Answer 3

Position
Flux
Magnitude
Colour
Spectral type
Lightcurve

Question 4

Describe 3 characteristics of electromagnetic radiation.

Answer 4

All EMR travels at the speed of light (c = 3x10^8 m/s)
It has wave-like properties; described by wavelength (lambda) or frequency (f), e.g interference.
It has particle-like properties; described in photons as ‘packets’ of energy, e.e photoelectric effect

Question 5

Write an equation to describe wave-like properties of EMR.

Answer 5

c = f * (lambda)

Question 6

Write an equation to describe particle-like properties of EMR.

Answer 6

E = hf or E =hc/lambda

h -> Planck’s constant

Question 7

If a body has a temperature higher than 0K what does this mean?

Answer 7

It is higher than -273C and it emits radiation.

Question 8

What depends on the temperature of the emitting body?

Answer 8

The wavelength, colour and intensity.

Question 9

Define blackbodies

Answer 9

An idealised body in thermodynamic equilibrium with surroundings. It absorbs all radiation incident and re-radiates it.

Question 10

Give 3 examples of blackbodies

Answer 10

• Toaster
• Black tarmac on a hot day
• An oven with a hole

Question 11

How is Planck’s function and blackbodies related?

Answer 11

A blackbody emits some energy at all wavelengths. This spectrum is described by Planck’s function which is the emitted flux as a function of frequency or wavelength.
At higher temperatures the peak of Planck’s function shifts towards shorter wavelengths.

Question 12

Describe the difference between hot and cold blackbodies.

Answer 12

At every wavelength a hotter blackbody emits more energy than a cooler one.

Question 13

Draw a graph showing Planck’s function

Answer 13

X-axis - wavelength
Y-axis - Flux or intensity
higher temperature line, peaks at a shorter wavelength and has a higher peak that lower temperatures.

Question 14

What is Wien’s law equation?

Answer 14

(lambda)Max . T = 0.0029mK

Question 15

Describe Wien’s law and what this means?

Answer 15

For a blackbody at temperature T, there is a wavelength (lambda)Max at which it radiates its maximum amount of energy. This relationship is WIen’s law.

Question 16

Are stars described as blackbodies?

Answer 16

Yes, but

• Energy can only escape from the very outer layer
• Stellar interior is very opaque to virtually all EMR.

Question 17

What is an effective temperature?

Answer 17

An effective temperature (Teff) is the temperature of a blackbody that wold emit the same amount of radiation as the star, allowing star temperatures to be calculated.

Question 18

Calculate example (lambda)Max values:
Sun = Teff 5800K
Hot star = Teff 12000K
Cold star = Teff 3000K

Answer 18

Sun 500nm
Hot star 250nm
Cold star 1000nm

Question 19

Why do stars have different colours?

Answer 19

Stars show different colours depending on their temperatures which affect the appearance of their Planck’s function graph which is the easiest way to visualise this.

Question 20

What colour is:
Sun
Hot star
Cold star

Answer 20

Sun - yellow
Hot star - blue
Cold star - red

Question 21

What are the units for Planck’s function?

Answer 21

W m-2 Hz-1 Ster-1

Question 22

What is the equation for Planck’s function?

Answer 22

B (V, T) = (2hv^3/c^2)/(e^hv/kT -1)

Question 23

Why do we use the Rayleigh-Jeans approximation and what is the equation?

Answer 23

For long wavelengths and small frequencies this approximation is used e.g it could be used to predict infinite energy towards large frequencies (UV catastrophe)

Question 24

Describe the Stefan-Boltzmann Law

Answer 24

This law helps to calculate the total energy emitted by a blackbody over all wavelengths, per second, per square metre of the surface of the blackbody.
Basically qualitatively this equates to energy emitted at every wavelength depends strongly on temperature.

Question 25

Explain the maths that occurs to allow the Stefan-Boltzmann law to occur

Answer 25

-Use Planck’s function
-Intergrate it and substitute hV/kT to X
-This eventually gives
E (T) = (sigma) T^4
(sigma) = 5.67 x10^-8 W m-2 K-4

Question 26

How does luminosity link to temperature and size?

Answer 26

L = 4(pi)R^2(sigma)Teff^4
L = luminosity
R = size (the numbers contribute to the spherical surface area using radius R)
T = temperature (Teff is used here)