Nuclear reactions: Energy-Mass equivalence, E=mc^2

What is a nuclear reaction?

Why does it occur?

How does it occur?

How are nuclear reactions different from chemical reactions?

A nuclear reaction involves a change in the composition of an atomic nucleus, resulting in the formation of one or more different atomic nuclei, along with the release of a significant amount of energy. This process is distinct from chemical reactions, which involve changes in the electron configuration of atoms, but not in the atomic nucleus itself

One particularly significant aspect of nuclear reactions is their incredibly high energy density. The energy released in nuclear reactions is millions of times greater than that released in chemical reactions. This energy comes from the conversion of mass into energy, as described by Albert Einstein's famous equation E=mc^2, where E is energy, m is mass, and c is the speed of light. This remarkable feature is what makes nuclear reactions the basis for nuclear power and nuclear weapons.

How do nuclear reactions proceed?

Nuclear reactions can proceed in two main ways:

Nuclear fission:

This process involves the splitting of a heavy atomic nucleus, such as uranium-235 or plutonium-239, into smaller nuclei, accompanied by the release of energy and additional neutrons. This is the principle behind nuclear power plants and atomic bombs.

Nuclear fusion:

The fusion of hydrogen atoms into helium in the Sun is a typical example. Fusion involves the combining of lighter atomic nuclei, such as hydrogen isotopes, to form heavier nuclei, accompanied by the release of a large amount of energy. This process powers the sun and other stars, and researchers are working on harnessing it for commercial energy production on Earth.

Role of thermodynamics and kinetics in nuclear reactions

Thermodynamics and kinetics play important roles in nuclear reactions. Thermodynamics helps to determine the feasibility, energetics, and equilibrium of nuclear reactions. It can be used to calculate the energy released or absorbed during a nuclear reaction, as well as to determine the stability of the resulting nucleus.

Kinetics, on the other hand, is important in determining the rate at which nuclear reactions occur. It can be used to study the speed at which radioactive decay processes occur, the rate of neutron capture or fission processes, and the dynamics of nuclear reactions in general.

Fusion of Hydrogen into Helium in the Sun: E = mc^2

The equation E=mc^2, formulated by Albert Einstein, states that the energy (E) of an object at rest is equal to its mass (m) times the speed of light (c) squared.

This equation indicates that mass and energy are interchangeable and that a small amount of mass can potentially be converted into a large amount of energy. In the context of the sun's energy production through nuclear fusion, hydrogen atoms (consisting of protons and electrons) combine to form helium atoms. This process, known as nuclear fusion, occurs in the sun's core under extremely high temperatures and pressure. During fusion, four hydrogen nuclei (protons) combine to form a helium nucleus, with the release of energy. This energy is primarily released in the form of high-energy photons, which eventually make their way to the sun's surface and radiate out into space as sunlight.

The process of nuclear fusion in the sun obeys the principles of mass-energy equivalence described by E=mc^2. The mass of the helium nucleus produced in the fusion reaction is slightly less than the total mass of the four hydrogen nuclei that combined to form it. This missing mass is converted into energy according to Einstein's equation, and it is this energy that powers the sun and provides the light and heat that sustains life on Earth. In other words, the mass lost during the fusion process is converted into the abundant energy that the sun radiates into space.

Reactions at Sun's core

4H ---- > He

Mass of 4 H atoms: 4.03130 AMU

?Mass of 1 He atom: 4.00268 AMU

1 Atomic Mass Unit (AMU) equals 1.67x10-27kgs

The difference between the mass of 4 H atoms and 1 He atom is 0.02862 AMU which is only 0.71% of the original mass. This small fraction of the mass is converted into energy. If 4 grams (1/8 ounce) of H are converted to He, only 2.8x10-3 grams of the mass is converted to energy:

How much energy is generated from converting such a tiny amount of mass? We can calculate by using Einstein's famous formula.

???E = mc2

???E = (2.8x10-3 grams) x c2

???E = (2.8x10-6 kgs) x (3x108m/sec)2

???E = 2.6x1011 joules

Enough energy to keep a 60-watt light bulb shining for over 100 years!

1 Atomic Mass Unit (AMU) equals 1.67x10-27kgs

Look at the magnitude of energy created by the sun

It fuses about 600 million tons of hydrogen every second, yielding 596 million tons of helium. The remaining four million tons of hydrogen are converted to energy, which makes the Sunshine.

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