Fusion & Stars (DP IB Physics)

Main sequence stars remain in equilibrium because fusion reactions generate radiation pressure which acts outwards and balances the inwards-acting gravitational force.

A protostar becomes a main sequence star when nuclear fusion reactions are initiated in its core and the inward force of gravity is balanced by the outward pressure from the fusion reactions.

True.

All stars follow the same initial stages in their life cycle:

1. Nebula (cloud of dust and gas)

2. Protostar

3. Main sequence star

The stages that follow depend on the mass of the main sequence star that forms.

The stages, in the correct order, in the life cycle of a star similar to the Sun are:

1. Nebula (cloud of dust and gas)

2. Protostar

3. Main sequence star

4. Red giant

5. Planetary nebula

6. White dwarf

A main sequence star turns into a red giant when hydrogen in the star's core begins to run out and the star begins to fuse helium into heavier elements.

False.

A high mass star will eventually explode as a supernova and become a neutron star or a black hole.

The stages, in the correct order, in the life cycle of a star with a mass larger than the Sun are:

1. Nebula (cloud of dust and gas)

2. Protostar

3. Main sequence

4. Red supergiant

5. Supernova

6. Black hole, or neutron star

A supernova is a large exploding star.

A supernova occurs when a star much more massive than the Sun reaches the end of its red supergiant stage. It collapses, becomes very unstable and explodes.

The mass of the remnant core determines whether a massive star becomes a neutron star or a black hole.

False.

High-mass stars have significantly shorter lifetimes than low-mass stars.

The greater the mass of a star, the higher its temperature, therefore, the greater the rate of fusion and the quicker the fuel is depleted in its core.

The Hertzsprung-Russell (HR) diagram is a plot of a star's luminosity on the y-axis and its surface temperature on the x-axis.

The star with the highest surface temperature is star B.

The hottest stars are located towards the left side of the H-R diagram.

The star with the coolest surface temperature is star D.

The coolest stars are located towards the right side of the H-R diagram.

The brightest star is star A.

The brightest stars are found near the top of the H-R diagram.

The most similar star to the Sun is star C.

The luminosity scale is given in solar units, where the luminosity of the Sun = 1

On the H-R diagram, main sequence stars are stars found in a band from the top left to the bottom right.

On the H-R diagram, white dwarfs are located below the main sequence and slightly to the left.

On the H-R diagram, red giants are located above the main sequence and slightly to the right.

The hottest and dimmest stars on the H-R diagram are white dwarfs.

The coolest and brightest stars on the H-R diagram are red supergiants.

The three types of light spectra are:

• continuous spectra

• emission spectra

• absorption spectra

False.

Absorption spectra are observed when white light passes through a cool, low-pressure gas.

True.

Continuous spectra are produced from hot, dense sources, such as the cores of stars.

Stars emit absorption spectra because:

• the hot, dense core produces a continuous spectrum

• the cool, low-density gas in the outer layers absorbs photons

• the resulting spectrum is a set of dark lines on a coloured background

The chemical composition of a star can be determined by analysing its absorption spectrum and identifying elements by their unique pattern of spectral lines.

One astronomical unit (AU) is the mean distance between the centre of the Earth and the centre of the Sun.

1 AU is equal to approximately 1.5 × 10¹¹ m.

One light-year is the distance travelled by light in one year.

1 ly is equal to approximately 9.5 × 10¹⁵ m.

One parsec is a unit of distance that gives a parallax angle of 1 second of an arc.

1 pc is equal to approximately 3.1 × 10¹⁶ m.

Stellar parallax is the displacement in the apparent position of a nearby star against a background of distant stars when viewed from different positions of the Earth during its orbit around the Sun.

False.

Stellar parallax is accurate for measuring distances up to about 100 parsecs.

The equation for calculating the distance to a star is:

Where

• = distance, measured in parsecs (pc)

• = parallax angle, measured in arcseconds (")

There are approximately 3.3 light-years in 1 parsec.

• 1 light–year is approximately 9.5 × 10¹⁵ m

• 1 parsec is approximately 3.1 × 10¹⁶ m

• therefore, 1 pc = = 3.26 ly

False.

The parallax angle decreases as the distance to a star increases.

The inverse square law of flux for a star is:

• = radiant flux intensity, measured in watts per metre (W m^-2)

• = luminosity of the star, measured in watts (W)

• = distance to star from Earth, measured in metres (m)

Wien's displacement law for a star is:

• = peak wavelength of a star's emission, measured in metres (m)

• = surface temperature of the star, measured in kelvin (K)

The Stefan-Boltzmann law for a star is:

• = luminosity of the star, measured in watts (W)

• = radius of the star, measured in metres (m)

• = surface temperature of the star, measured in kelvin (K)

• = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴)

False.

The radius of a star cannot be directly measured but must be calculated using other observable properties.

To calculate the radius of a star using the Stefan-Boltzmann law:

• surface temperature can be calculated using Wien’s displacement law

• luminosity can be calculated using the inverse square law of flux equation

The star has a luminosity of

• Stefan-Boltzmann law:

• luminosity of the Sun:

• luminosity of the star:

• luminosity of the star:

The surface of star X is about 6 times hotter than that of star Y.

• Stefan-Boltzmann law:

• star X has a luminosity of and a radius of

• star Y has a luminosity of and a radius of

• ratio of temperatures:

• ratio of temperatures: