E5 - Nuclear Fusion

Nuclear Fusion

The joining of two small nuclei to produce a larger nucleus.

• A huge amount of energy is released in the reaction.

• Provides radiation pressure to stop a star from collapsing under its gravity.

What happens when 2 protons fuse.

1. A deuterium nucleus is formed.

2. In the center of the stars, the deuterium combines with a tritium nucleus to form a helium nucleus.

3. The total mass of the helium nucleus is less than the total mass of the individual nucleon.

4. Hence, the reaction releases energy, which provides fuel for the star to continue burning.

What are the conditions of fusion?

1. Both nuclei must have high kinetic energy.

• Nuclei must overcome the repulsive coulomb forces between protons.

• The strong nuclear force, which binds nuclei together, has a very short range.

2. Very high temperature.

3. Very high pressure and density.

Energy release in fusion reactions

When undergoing fusion reaction, the single larger nucleus produced will have a higher binding energy per nucleon than the original two nuclei.

• Because of the mass defect between the parent nuclei and the daughter nucleus, energy is released.

5 stages of fusion in stars

1. two protons fuse.

2. one proton changes into a neutron, as in beta-plus decay, to leave a deuterium nucleus.

3. another proton joins on making a nucleus of He-3.

4. two He-3 nuclei fuse.

5. two protons break off leaving an He-4 nucleus.

Nuclear fusion process of hydrogen nuclei to form helium nuclei

1. Four hydrogen nuclei (protons) are fused into one helium nucleus.

2. Producing two gamma-ray photons, two neutrinos, and two positrons.

3. Causes a massive amount of energy to release.

4. The momentum of the gamma-ray photons result in an outward acting pressure called radiation pressure.

Equilibrium process in stars

1. Once core temperature of stars reach millions of degree kelvin and the fusion of hydrogen nuclei to helium nuclei begins.

2. Protostars gravitational field continues to attract more gas and dust, increasing the temperature and pressure of core.

3. More frequent collisions = kinetic energy of particles increases = increasing the probability that fusion will occur.

4. When core becomes hot enough, fusion reaction can start, they will begin to produce an outward radiation pressure = balance with inwards pull of gravity.

5. Star reaches an equilibrium where inward and outward forces are in equilibrium.

6. As the temperature of the star increases, its volume decreases due to gravitational collapse = gas pressure increases.

7. The gas pressure and radiation pressure act outward to balance gravitational force (F = mg) acting inwards.

8. If temp increases = outward pressure increases = star expands.

9. If temp decreases = outward pressure decreases = star contracts.

Initial stages for life cycle of a star

1. Nebula: all stars form from a giant cloud of hydrogen gas and dust.

• Gravitational attraction between individual atoms forms denser clumps of matter.

• This inward movement of matter is called gravitational collapse.

2. Protostar: the gravitational collapse causes the gas to heat up and glow.

• Work done on the particles of gas and dust by collision between the particles causes an increase in their kinetic energy, resulting in an increase in temperature

• These stars are detected by telescopes with infrared radiation.

• Temperature reaches millions of degrees and fusion of hydrogen nuclei to helium nuclei begins.

• The protostar’s gravitational field attracts more dust and gas = increase in temperature and pressure.

• More frequent collisions, the kinetic energy of the particles increases, increasing probability that fusion will occur.

3. Main sequence star:

• The star reaches a stable state where the inward and outward forces are in equilibrium.

• As the temperature of the star increases, its volume decreases due to gravitational collapse, and the gas pressure increases.

Next stages for low mass stars

1. Red Giant: Hydrogen supplies in core begins to run out, as most of the star has been fused into helium = nuclear fusion slows down = energy released by hydrogen fusion decreases, but it continues in the shell around the core.

• The star initially shrinks which causes core to become hotter = when temp increases helium fusion begins = releases massive amounts of energy which causes the outer layers to swell and cool to form a red giant.

2. Planetary Nebula: Helium supply in the core begins to run out = core contracts, but it doesn’t get hot enough for another fusion reaction. The outer layers of the star are released.

3. White Dwarf: The solid core collapses under gravity. The remnant left behind is a very hot, dense core called a white dwarf.

Next stages for massive stars

1. Red Super Giant: the star follows the same process as the formation of a red giant.

• The shell-burning and core-burning cycle in massive stars goes beyond that of low-mass stars, fusing elements up to iron.

2. Supernova: the iron core collapses, the outer shell is blown out in an explosive supernova.

3. Neutron star (or Black Hole): after the supernova explosion, the collapsed neutron core can remain intact having formed a neutron star.

• If remnant core has a mass greater than 3 times the solar mass, the pressure becomes so great that it collapses and produces a black hole.

What does the Hertzsprung-Russel (HR) Diagram show?

Plotting of the luminosity of different stars against their temperatures.

What are conditions for main sequence stars?

Luminosity increases with surface temperature.

What are conditions for Red Giants and Red Super Giants?

Luminosity increases at cooler temperatures.

What are conditions for White Dwarf Stars?

Luminosity decreases at higher temperatures.

Continuous spectra

Photons are emitted from the core of a star containing all the wavelengths and frequencies of the electromagnetic spectrums, in hot and dense sources.

Emission spectra

When an electron transitions from a higher energy level to a lower energy level, this results in the emission of a photon, in hot and low-pressure gases.

Absorption spectra

When an electron transitions from a lower energy level to a higher energy level, this results in the absorption of a photon, in a cool and low-pressure gas.

Astronomical Unit

The mean distance from the center of the Earth to the center of the sun.

Light year

The distance travelled by light in one year.

Parsec

Unit of distance that gives a parallax angle of 1 second of an arc (of a degree), using the radius of the Earth’s orbit (1 AU) as the baseline of a right angled triangle.

Stellar parallax

Apparent shifting in position of a nearby star against a background of distant stars when viewed from different positions of the Earth, during the Earth’s orbit about the Sun.

How can the radius of a star be estimated?

By combining Wien’s displacement law and the Stefan-Boltzmann law (inverse square law of flux).