SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

PHYSICS, M8 2023 HSC 21

A Hertzsprung–Russell diagram is shown.
 

  1. Identify TWO variables that determine the luminosity of a star  (2 marks)
  1. Describe differences between stars \(A\) and \(B\).  (3 marks)
Show Answers Only

a.    The luminosity of a star can be determined by its size and temperature.

Other variables could include:

→ Mass, colour and the power output of a star.
 

b.   Differences:

→ Star A is a main sequence star and is therefore fusing hydrogen to helium in its core via both the proton-proton chain and CNO cycle whereas Star B is a white dwarf star and therefore has no fusion taking place in its core.

→ Star A has a greater luminosity compared to Star B.

→ Star A is a younger star then Star B which is at the end of its lifecycle. 

Other differences could include:

→ Mass

→ Radius or size

Show Worked Solution

a.    The luminosity of a star can be determined by its size and temperature.

Other variables could include:

→ Mass, colour and the power output of a star.
 

b.   Differences between stars:

→ Star A is a main sequence star and is therefore fusing hydrogen to helium in its core via both the proton-proton chain and CNO cycle whereas Star B is a white dwarf star and therefore has no fusion taking place in its core.

→ Star A has a greater luminosity compared to Star B.

→ Star A is a younger star then Star B which is at the end of its lifecycle.
 

Other differences could include:

→ Mass

→ Radius or size

PHYSICS, M8 EQ-Bank 6 MC

The Hertzsprung-Russell diagram shown is used to classify stars.
 

Stars in region `S` of the diagram are much dimmer than other stars in the same spectral class.

What property of the stars in region `S` explains their relatively low luminosity?

  1. They are cooler than other stars.
  2. They have a smaller mass than other stars.
  3. They have a smaller surface area than other stars.
  4. They are further away from Earth than other stars.
Show Answers Only

`C`

Show Worked Solution

By elimination:

→ All stars in the same spectral class have similar temperatures (eliminate A).

→ Stars become white dwarves when they no longer are able to fuse elements to generate energy. The outer gaseous layers are expelled and only the hot, dense core is left. In this way, white dwarves do not have significantly lower masses compared to other stars (eliminate B).

→ Luminosity refers to the total energy radiated by a star per second and is independent on a star’s distance from Earth (eliminate D).

`=>C`

PHYSICS, M8 EQ-Bank 1 MC

A Hertzsprung-Russell diagram is shown.
 

In which region would a star have the same surface temperature as a star on the main sequence?

  1. `P`
  2. `Q`
  3. `R`
  4. `S`
Show Answers Only

`D`

Show Worked Solution

→ Using the `x`-axis of the Hertzsprung-Russel diagram, `S` is the only region in which stars have the same surface temperature as a star on the main sequence.

`=>D`

PHYSICS, M8 2015 HSC 33d

The position of the Sun, star `W` and star `Z` are shown on the H-R diagram.
 

The curves `A` and `B` show intensity versus frequency for star `W` and the Sun, measured from the same distance.
 

  1. Identify which curve (`A` or `B`) represents star `W` and justify your choice.   (2 marks)
  1. Account for differences between stars `W` and `Z` that can be deduced from the H-R diagram.   (3 marks)
Show Answers Only

i.    → Curve A represents star `W`.

→ `W` is hotter so will emit more energy overall, and peak frequency will be higher.
 

ii.   Differences displayed in H-R graph:

→ Star `W` lies in the main sequence and is therefore fusing hydrogen to helium, most likely via CNO cycle as it is a large dense star.

→ Star `Z` is past main sequence and is therefore fusing larger elements.

→ Since star `Z` is cooler than `W` (refer to its H-R diagram location ) but has similar luminosity, we can deduce it is much larger than `W`.
 

Other possible answers could include:

→ Differences in fuel source, size and temperature of the stars.

Show Worked Solution

i.    → Curve A represents star `W`.

→ `W` is hotter so will emit more energy overall, and peak frequency will be higher.
 

ii.   Differences displayed in H-R graph:

→ Star `W` lies in the main sequence and is therefore fusing hydrogen to helium, most likely via CNO cycle as it is a large dense star.

→ Star `Z` is past main sequence and is therefore fusing larger elements.

→ Since star `Z` is cooler than `W` (refer to its H-R diagram location ) but has similar luminosity, we can deduce it is much larger than `W`.
 

Other possible answers could include:

→ Differences in fuel source, size and temperature of the stars.

PHYSICS, M8 2016 HSC 33e

Describe how the distribution of stars on a Hertzsprung-Russell diagram relates to the processes that occur during their evolution.   (6 marks)

Show Answers Only

→ An H-R diagram distributes stars into different groupings that relate to the processes that occurred during their evolution.

→ Hydrogen fusion is the primary source of energy of stars on the main sequence.

→ Hydrogen fusion is replaced by helium fusion as the main source of energy in the star’s next evolutionary phase. This grouping of stars is also known as red giants.

→ After helium fusion, the next evolutionary stage for most stars involves gravitational collapse. At this stage, the surface of the star recedes and gravitational potential energy is converted to radiant energy. This grouping is known as white dwarfs.

→ A star’s transition between evolutionary phases occurs quickly relative to time spent in each group. 

→ This transition speed results in fewer stars being distributed in areas outside of these groups on the H-R diagram.
 

Other possible answers could include:

→ Reference to other groups such as protostars, supergiants

→ Sketch of H-R diagram

→ Reference to properties of stars related to their distribution within particular groups

→ Globular and open clusters.

Show Worked Solution

→ An H-R diagram distributes stars into different groupings that relate to the processes that occurred during their evolution.

→ Hydrogen fusion is the primary source of energy of stars on the main sequence.

→ Hydrogen fusion is replaced by helium fusion as the main source of energy in the star’s next evolutionary phase. This grouping of stars is also known as red giants.

→ After helium fusion, the next evolutionary stage for most stars involves gravitational collapse. At this stage, the surface of the star recedes and gravitational potential energy is converted to radiant energy. This grouping is known as white dwarfs.

→ A star’s transition between evolutionary phases occurs quickly relative to time spent in each group. 

→ This transition speed results in fewer stars being distributed in areas outside of these groups on the H-R diagram.
 

Other possible answers could include:

→ Reference to other groups such as protostars, supergiants

→ Sketch of H-R diagram

→ Reference to properties of stars related to their distribution within particular groups

→ Globular and open clusters.


♦♦ Mean mark 44%.

PHYSICS, M8 2017 HSC 33bi

The diagram shows the positions of stars `X` and `Y` on a H-R diagram.
 

     

Outline the differences in the spectra of stars `X` and `Y`.   (2 marks)

Show Answers Only

→ Star \(\text{X}\): the H-R diagram exhibits the highest intensity in the blue part of the spectrum (short wavelength) with ionised \(\ce{He}\) lines and strong UV component.

→ Star \(\text{Y}\): its highest intensity appears in the red part of the spectrum (long wavelength) with dominant molecular lines and strong neutral metal lines.

Show Worked Solution

→ Star \(\text{X}\): the H-R diagram exhibits the highest intensity in the blue part of the spectrum (short wavelength) with ionised \(\ce{He}\) lines and strong UV component.

→ Star \(\text{Y}\): its highest intensity appears in the red part of the spectrum (long wavelength) with dominant molecular lines and strong neutral metal lines.


♦♦ Mean mark 36%.

PHYSICS, M8 2018 HSC 33c

A H–R diagram is shown. Star `X` is a main sequence star of 12 solar masses.
 

Describe how star `X` will change physically and chemically as it continues to evolve.   (4 marks)

Show Answers Only

→ Star `X` is a hot, blue-white B-class giant that is fusing Hydrogen to Helium in its core. It will have a relatively short life span in its current state.

→ Its next evolutionary stage will be a red supergiant where its size will increase dramatically although its luminosity would stay the same.

→ At this next stage, Helium burning starts in the core and changes to fusion between helium and carbon to form oxygen.

→ As the temperature rises carbon fuses to form heavier elements such as iron. This eventually causes the core to collapse forming a supernova explosion.

→ The explosion results in an increase in its luminosity and eventually to a gravitational collapse into a black hole.

Show Worked Solution

→ Star `X` is a hot, blue-white B-class giant that is fusing Hydrogen to Helium in its core. It will have a relatively short life span in its current state.

→ Its next evolutionary stage will be a red supergiant where its size will increase dramatically although its luminosity would stay the same.

→ At this next stage, Helium burning starts in the core and changes to fusion between helium and carbon to form oxygen.

→ As the temperature rises carbon fuses to form heavier elements such as iron. This eventually causes the core to collapse forming a supernova explosion.

→ The explosion results in an increase in its luminosity and eventually to a gravitational collapse into a black hole.


♦ Mean mark 42%.

PHYSICS M8 2022 HSC 21

The positions of two stars, `X` and `Y`, are shown in the Hertzsprung-Russell diagram.
 

  1. Compare qualitatively the surface temperature and luminosity of `X` and `Y`.  (2 marks)

  1. Identify the elements undergoing fusion in the core of each star, `X` and `Y`.  (2 marks)
Show Answers Only

a.   Surface Temperature: The surface temperature of `X` is greater than the surface temperature of `Y.`

Luminosity: The luminosity of `Y` is greater than the luminosity of `X.`
 

b.   → `X` is a main sequence star so in its core hydrogen is being fused into helium.

→ `Y` is a red giant so in its core helium is being fused into carbon.

Show Worked Solution

a.   Surface Temperature:

→ The surface temperature of `X` is greater than the surface temperature of `Y.`

Luminosity:

→ The luminosity of `Y` is greater than the luminosity of `X.`
 

b.    → `X` is a main sequence star so in its core hydrogen is being fused into helium.

→ `Y` is a red giant so in its core helium is being fused into carbon.

PHYSICS, M8 2019 HSC 4 MC

Four stars, `P`, `Q`, `R` and `S`, are labelled on the Hertzsprung-Russell diagram.
 

Which statement is correct?

  1. `S` has a greater luminosity than `Q`.
  2. `R` is a blue star whereas `S` is a red star.
  3. `S` has a higher surface temperature than `R`.
  4. `P` is at a more advanced stage of its evolution than `R`.
Show Answers Only

`C`

Show Worked Solution

Stars further to the left of the Hertzsprung-Russell diagram have greater surface temperatures.

`=>C`

PHYSICS, M8 2020 HSC 6 MC

The Hertzsprung-Russell diagram shows characteristics of stars in a globular cluster 100 light years in diameter and 27 000 light years from Earth.
 

The stars plotted on this Hertzsprung-Russell diagram have approximately the same

  1. age.
  2. colour.
  3. luminosity.
  4. mass.
Show Answers Only

`A`

Show Worked Solution

The `x`-axis indicates the stars have varying colour and mass.

The `y`-axis indicates the stars vary in luminosity. These variations indicate the stars also vary in mass.

The fact that the stars are found in a cluster suggests they are of a similar age.

`=> A`


♦ Mean mark 41%.