smc-3699-80-E = mc^2

A system consists of a sealed glass jar containing some oxygen and a small strip of magnesium.

The magnesium reacts with the oxygen to produce magnesium oxide as a product. Energy is released from the system in this reaction.

The mass of the system will

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\(B\)

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Option \(B\) is correct.

The system is sealed, so no matter enters or leaves – the magnesium and oxygen simply rearrange into magnesium oxide inside the jar.
Energy is released from the system and according to Einstein’s mass-energy equivalence \((E = mc^2)\), this lost energy corresponds to a decrease in mass.

Other options:

\(A\) is incorrect. No oxygen is added – it was already in the sealed jar.
\(C\) is incorrect. Energy is released (removed), not added to the system.
\(D\) is incorrect. No magnesium or oxygen is lost – they’re converted to magnesium oxide within the sealed system.

\(\Rightarrow B\)

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

Justify this statement. (7 marks)

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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.

`E`	`=mc^2`
`m`	`=(E)/(c^(2))=(2.31 xx10^(30))/((3xx10^(8))^(2))=2.57 xx10^(13)\ \text{kg}`

PHYSICS, M7 2025 HSC 19 MC