# Disintegration Energy in Nuclear Physics: Definition & Formula

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• 0:01 What Is Disintegration Energy?
• 1:01 Mass-Energy Equivalence
• 2:28 Example
• 4:18 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you should be able to explain what disintegration energy is and use mass-energy equivalence to calculate the disintegration energy in a nuclear decay reaction.

## What Is Disintegration Energy?

Disintegration energy is the energy released during radioactive decay. Nuclear physics involves the study of many nuclear reactions, where one atom or particle turns into another, or where particles collide, creating new ones. These reactions are on a tiny scale, but can be super dramatic, absorbing or creating huge quantities of energy. Some of these reactions are called radioactive decay reactions.

Radioactive decay is where an unstable atomic nucleus decays or turns into a more stable nucleus, releasing energy in the form of ionizing particles and radiation. These ionizing particles include alpha particles and beta particles, and the radiation includes the famous gamma rays that created the Hulk. Unfortunately, gamma rays don't really do that, but radioactive materials really do emit a lot of energy. And that disintegration energy, the energy produced as the atom. . . I suppose, disintegrates. . . into another, is what we're talking about today. In order to discuss that, we need to take a look at Einstein's most famous equation.

## Mass-Energy Equivalence

In physics, it is understood that mass and energy are really the same thing, viewed from different perspectives. An object with more energy will be measured as having more mass. An object with more mass contains more energy. This idea of mass-energy equivalence is represented by Einstein's famous E = mc^2 equation, where E is the energy in Joules; m is the mass in kilograms; and c is the speed of light in meters per second, which is always 3 x 10^8.

This equation tells us that if energy leaves a nucleus, its mass will change. If we weigh it, it will weigh less than it did. In a nuclear reaction, the number of protons, neutrons and electrons stay the same before and after. So, how can the mass be changing?

The important thing to realize is that protons, neutrons and electrons weigh more individually than they do when combined into atoms. An atom containing two protons, two neutrons and two electrons will have a smaller mass than all those particles on their own. This is because energy is released when atoms are created, and energy is used up when atoms are pulled apart.

So in any nuclear reaction, if you compare the mass of the reactants with the mass of the products, the difference in those values will tell you: a) whether energy was absorbed or released and b) how much energy that was. This comparison of masses is how we calculate the disintegration energy.

## Example

Let's go through an example. Here is an equation for a decay reaction called alpha decay:

It's called that because it produces an alpha particle, otherwise known as a helium nucleus. Radium-223 has an atomic weight of 223.01850 u. U stands for atomic mass units. A helium nucleus has an atomic weight of 4.001505 u, and Radon-218 has an atomic weight of 218.005601 u. You're asked to calculate the energy released in the reaction in Joules. Note that 1 atomic mass unit is equal to 1.66 x 10^-27 kilograms.

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