Nuclear Energy

In the 21st Century, the concept of nuclear energy is not strange to most people. Generally speaking, people know about nuclear bombs and nuclear power plants. Many people can explain that the sun (that stars) are giant nuclear plants that give off energy.

In the 1990s, the band, They Might Be Giants produced a song that stated:

The sun is mass of incandescent gas, a gigantic nuclear furnace
Where hydrogen is built into helium at a temperature of millions of degrees

-- They Might Be Giants - "Why Does the Sun Shine? (The Sun is a Mass of Incandescent Gas)"


So, how exactly does nuclear energy work? 

This goes back to the four basic forces that exist. Some people will recall they are:

gravitational
electromagnetic
strong (nuclear)
weak (nuclear)

Nuclear energy is associated with the last two. It takes a lot of energy to hold an atom together. That energy can be released when the atom is split.

Nuclear fission, the splitting of an atom's nucleus, releases a great deal of stored energy by… we'll get to that in a moment.

Another process related to the nucleus (hence the term nuclear) is when two or more nuclei are shoved together. This also results in the release of a great deal of energy!

Nuclear fusion, the joining of two or more atom's nuclei, releases energy by… stand by! Getting to that soon.

Both fission and fusion release energy. But how? And why so much?

Fission and fusion both involve altering the nuclei of atoms. Fission splits a nucleus and fission joins two or more. It is important to note that both fission and fusion result in atoms that have different atomic numbers (number of protons) than the original elements. For instance fusing hydrogen (atomic number 1) results in heliums (atomic number 2).

Something else happens when fission and fusion take place. Those of you who like to break the laws will really like this! (Note: breaking laws is agains the law and should not be done, ever. Unless you are fission or fusion.)

The law of conservation of matter is broken. The mass before and after nuclear reactions is different. The law of conservation of matter says that matter cannot be created or destroyed. Well…

There is also a law of conservation of energy that says that energy cannot be created or destroyed--that it only changes form. Well…

The processes of fission and fusion do not follow these laws. BUT!! The change in mass and the change in energy are related. In fact, they are exactly connected. Not only is the change in mass and energy connected, but they are connected by the most famous physics formula ever!

E = mc²

Yep!

This is what you've been waiting for ever since you first discovered Einstein's most famous formula!

So what does that mean?

It means that the conversion of matter to energy joins with the laws of conservation to result in a new, combined law:

The total of mater and energy is a constant never changing, but possibly interchanging.


Back to fusion and fission…

In nuclear reactions (both fission and fusion), energy is released (here are the conclusions) …by converting some amount of matter into energy. The amount of energy released is found using the equation

E = mc²

where E is the energy given off in joules, m is the mass in kilograms, and c is the speed of light (also the speed of an electromagnetic wave [energy]) which is a constant:

c = 299 792 458 m / s 

Now, nearly never is c written that way. The normal procedure is to write it in scientific notation as: 

c = 3 X 10⁸ m/s 

So, who doesn't like exponential notation? 

Working with the equation is not difficult. Find c²  then multiply by the mass. Done.


DIVERSION INTO MATH

So, a review of finding the square in exponential notation seems in order…

Let's find y where:

y = x²

and x = 200

y = x²
y = 200²
y = 40,000

Now, 200 = 2  X  10²

So…
y = x²
y = 200²
y = (200)²
y = (2  X  10²)²

Recall that to raise an exponent to the power of an exponent, you multiply exponents. thus…

y = (2  X  10²)²
y = 4  X  10⁴

It is fine to leave the equation above as is, but for the sake of proof, we can take it one more step:

y = 4  X  10⁴
y = 40,000


BACK TO NUCLEAR ENERGY

Working with the equation

E = mc²

is not difficult. Find c²  then multiply by the mass. Done.

Thus,  given any mass in kilograms, multiply by c² to find the amount of energy in joules that is given off. Finding c² and working out examples is left as an exercise for the reader.

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REFERENCES:

https://www.studentenergy.org/topics/nuclear

https://www.pbs.org/wgbh/nova/einstein/lrk-hand-emc2expl.html