In nuclear reactions, the energy produced is related to mass by which famous relation?

Introduction / Context:
Nuclear reactions, such as fission and fusion, release enormous amounts of energy. A key idea in modern physics is that mass and energy are interchangeable, and even a small mass can correspond to a very large amount of energy. This question asks you to identify which relation describes this mass energy equivalence, a cornerstone of nuclear physics and relativity.

Given Data / Assumptions:

• We are dealing with energy produced in nuclear reactions.
• Options list several gas laws and one relation involving mass and energy.
• We assume you know basic gas laws from thermodynamics and the famous formula from relativity.
• The task is to pick the law that directly connects mass and energy.

Concept / Approach:
The mass energy relation introduced by Einstein states that energy E is equal to mass m multiplied by the square of the speed of light c, usually written as E = m * c^2. This means that a small decrease in mass during a nuclear reaction can produce a large release of energy. The other laws mentioned, such as Charles law, Boyle law, Gay Lussac law, and Graham law, deal with gases, volumes, pressures, and diffusion, not with mass energy equivalence.

Step-by-Step Solution:
Step 1: Recall that in nuclear fission or fusion, the total mass of products is slightly less than the total mass of reactants. Step 2: The missing mass, called mass defect, is converted into energy. Step 3: Einstein mass energy relation states E = m * c^2, where c is the speed of light in vacuum. Step 4: Because c is very large, squaring it makes even a small mass convert into a huge amount of energy, which explains the power of nuclear reactors and atomic bombs. Step 5: Charles law and Boyle law relate gas volume to temperature or pressure, and do not mention mass and energy directly. Step 6: Therefore, the energy produced in a nuclear reaction is described by the Einstein mass energy relation.

Verification / Alternative check:
Textbooks on nuclear physics and modern physics always cite the formula E = m * c^2 when discussing nuclear binding energy and mass defect. Examples show that calculating the mass difference between reactants and products and then applying E = m * c^2 yields the energy released. None of the classical gas laws can be used for such calculations. This strong association of nuclear energy with the mass energy relation confirms that Einstein relation is the correct answer.

Why Other Options Are Wrong:
Charles law: States that for a fixed mass of gas, volume is directly proportional to temperature at constant pressure; it does not relate mass and energy.
Graham law: Deals with the rate of diffusion of gases and says that rate is inversely proportional to the square root of density; again no mass energy relation.
Gay Lussac law: Relates pressure and temperature of gases at constant volume; not relevant to nuclear energy.
Boyle law: States that for a fixed mass of gas, pressure is inversely proportional to volume at constant temperature; it does not involve conversion of mass into energy.

Common Pitfalls:
A common mistake is to quickly choose a familiar gas law without reading the question carefully. The key words here are nuclear reaction and energy produced. Whenever these appear together, you should think of mass defect and the relation E = m * c^2. Remember that gas laws are about macroscopic properties of gases, while the mass energy relation is about fundamental equivalence of mass and energy in nuclear and high energy processes.

Final Answer:
The energy produced in nuclear reactions is explained by the Einstein mass energy relation, E = m * c^2.