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PHYSICS, M8 2020 VCE 13 MC

Matter is converted to energy by nuclear fusion in stars.

If the star Alpha Centauri converts mass to energy at the rate of 6.6 × 10\(^9\) kg s\(^{-1}\), then the power generated is closest to

  1. \(2.0 \times 10^{18}\ \text{W}\)
  2. \(2.0 \times 10^{18}\ \text{J}\)
  3. \(6.0 \times 10^{26}\ \text{W}\)
  4. \(6.0 \times 10^{26}\ \text{J}\)
Show Answers Only

\(C\)

Show Worked Solution
  • The energy produced by the star each second is the power generated by the star.
  • \(E=mc^2=6.6 \times 10^9 \times (3 \times 10^8)^2=6 \times 10^{26}\ \text{Js}^{-1}=6 \times 10^{26}\ \text{W}\)

\(\Rightarrow C\)

Mean mark 56%.

Filed Under: Origins of Elements Tagged With: Band 4, smc-3700-60-Mass-Energy Equivalence

PHYSICS, M8 EQ-Bank 22

Einstein's equation `E = mc^(2)`  is one of the most important equations in the history of physics.

Justify this statement.   (7 marks)

--- 14 WORK AREA LINES (style=lined) ---

Show Answers Only

Position Statement

  • Einstein’s equation `E=mc^2` is among physics’ most important equations because it reveals mass-energy equivalence and explains fundamental processes from atomic to cosmic scales.

Nuclear Applications

  • The equation explains energy from nuclear fission and fusion processes. It shows how tiny amounts of matter convert to enormous energy in nuclear reactions.
  • The mass defect in atoms directly relates to binding energy through `E=mc^2` and this principle drives nuclear reactors that power cities and nuclear weapons.
  • These applications are responsible for revolutionising both energy production and global politics.

Cosmic and Particle Physics

  • Stars produce energy by converting mass to energy through fusion reactions. The Sun converts 4 million tonnes of mass to energy every second using this principle
  • Particle accelerators create new particles by converting kinetic energy into mass. This allows scientists to study fundamental matter structure and discover new particles.
  • Furthermore, mass dilation near light speed also follows from this mass-energy relationship.

Reinforcement

  • While other equations like Newton’s gravity law are important, they lack the broad applicability of `E=mc^2`.
  • No other single equation explains phenomena from subatomic particles to stellar processes.
  • The equation unified our understanding of matter and energy as different forms of the same thing.
  • This justifies calling `E=mc^2` one of history’s most important physics equations.
Show Worked Solution

Position Statement

  • Einstein’s equation `E=mc^2` is among physics’ most important equations because it reveals mass-energy equivalence and explains fundamental processes from atomic to cosmic scales.

Nuclear Applications

  • The equation explains energy from nuclear fission and fusion processes. It shows how tiny amounts of matter convert to enormous energy in nuclear reactions.
  • The mass defect in atoms directly relates to binding energy through `E=mc^2` and this principle drives nuclear reactors that power cities and nuclear weapons.
  • These applications are responsible for revolutionising both energy production and global politics.

Cosmic and Particle Physics

  • Stars produce energy by converting mass to energy through fusion reactions. The Sun converts 4 million tonnes of mass to energy every second using this principle
  • Particle accelerators create new particles by converting kinetic energy into mass. This allows scientists to study fundamental matter structure and discover new particles.
  • Furthermore, mass dilation near light speed also follows from this mass-energy relationship.

Reinforcement

  • While other equations like Newton’s gravity law are important, they lack the broad applicability of `E=mc^2`.
  • No other single equation explains phenomena from subatomic particles to stellar processes.
  • The equation unified our understanding of matter and energy as different forms of the same thing.
  • This justifies calling `E=mc^2` one of history’s most important physics equations.

Filed Under: Light and Special Relativity, Origins of Elements, Properties of the Nucleus Tagged With: Band 3, Band 4, Band 5, smc-3699-80-E = mc^2, smc-3700-60-Mass-Energy Equivalence, smc-3703-20-Conservation of Mass-Energy

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)

--- 4 WORK AREA LINES (style=lined) ---

  1. Account for differences between stars `W` and `Z` that can be deduced from the H-R diagram.   (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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.

Filed Under: Origins of Elements Tagged With: Band 3, Band 4, smc-3700-10-H-R Diagrams, smc-3700-60-Mass-Energy Equivalence

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