Exam Qs: Classification of stars

Question 1

discuss how the HR diagram, together with Stefan’s law, shows that the size of the sun will vary during the next stages of its life cycle. Include a sketch of the HR diagram in your answer (6)

Answer 1

sketch of HR diagram including the main sequence, giants, and white dwarfs indicated in correct places. Correct labels for the axes and directions for which scales increase or decrease are shown.

brighter a star, the more energy it emits as EM radiation, and so the greater power, P.

description of Stefan’s law

after the main sequence, the sun will become a red giant, moving upwards and right from its position in the main sequence to the giants on the HR diagram.

Temperature of star will decrease, but a change in absolute magnitude means the power will increase significantly

so by Stefan’s law, for there to be an increase in power, but a decrease in temperature, the surface area of the star must increase significantly

when the sun evolves from a red giant to a white dwarf, it will move down and to the left of the HR diagram, becoming much hotter, but much less luminous than when it was a red giant.

Since P = σAT⁴, if it gets much hotter, but power gets much smaller, then the surface area must get significantly smaller,

SO the sun’s size will vary greatly throughout its remaining lifetime

Question 2

State what is meant by a black body and explain why assuming a star to be a black body allows scientists to estimate the stars temperature (2)

Answer 2

A black body is an object that completely absorbs all EM radiation that is incident on it.

The colour / continuous spectrum / wavelength of maximum intensity are things that can be reliably recorded from stars. For black bodies, these properties depend only on temperature and so, by assuming a star as a black body, the temperature of the star can be calculated from these observations

Question 3

A Balmer absorption line from a distant galaxy has a wavelength of 697 nm

the galaxy is 290 Mpc from Earth

calculate the wavelength of the absorption line if it was produced and measured in a laboratory on Earth (4)

Answer 3

Using -Δλ/λ = v/c

then substituting v = HD into equation but as -HD because of red shift

re arranging for λ gives 660nm (3 s.f.)

Question 4

Star A has an absolute magnitude of -1.46 and star B has an absolute magnitude of +1.54

Calculate the ratio:

(intensity of star A) / (intensity of star B)

(2)

Answer 4

A difference of 1 on the magnitude scale corresponds to an intensity ratio of 2.51

difference between A and B is 3

intensity of star A / intensity of star B

= 2.51³ = 15.8 (3sf)