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# Nuclear Equations

## A reaction that changes the atomic nucleus. Examples: fusion and fission.

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Nuclear Reactions

Credit: Courtesy of the US Department of Energy
Source: http://commons.wikimedia.org/wiki/File:Castle_romeo2.jpg

Operation Castle was a series of nuclear tests that the United States conducted in 1954 in the Bikini and Enewetok atolls in the Marshall Islands of the Pacific. The purpose of the tests was to validate the designs of different thermonuclear weapons.

### Nuclear Reactions

In all nuclear reactions, the total of the atomic numbers on the left side of the equation must equal the total of the atomic numbers on the right side of the equation. Furthermore, the sum of the mass numbers on the left of the equation must equal the sum of the mass numbers on the right of the equation. In addition to alpha and beta decay, there are a number of other types of nuclear reactions. Bombardment of nuclei with alpha particles or neutrons can often produce a nuclear reaction. Consider the bombardment of nitrogen-14 by an alpha particle,

\begin{align*}{^4_2 \text{He}}+{^{14}_{\phantom{0}7} \text{N}} \rightarrow {^1_1 \text{H}}+{^{17}_{\phantom{0}8} \text{O}}\end{align*}

or the bombardment of uranium-235 by a neutron.

\begin{align*}{^{235}_{\phantom{0}92}\text{U}}+{^1_0 n} \rightarrow {^{89}_{36} \text{Kr}} + {^{144}_{\phantom{0}56} \text{Ba}}+3 \ {^1_0 n}\end{align*}

Large unstable nuclei often become more stable by breaking into smaller pieces. The breakup of a larger nucleus into two or more smaller nuclei is called fission. Small nuclei often become more stable by joining together to form larger nuclei. This process is called fusion.

Here is a reaction showing the fusion of a hydrogen-2 atom and a hydrogen-3 atom.

\begin{align*}{^2_1 \text{H}}+{^3_1 \text{H}} \rightarrow {^4_2 \text{He}}+{^1_0 n}\end{align*}

The disintegration of unstable nuclei does not occur all at once. The rate of disintegration is a statistical process. The most convenient way to consider it is by a concept known as half-life. The time required for half of the atoms in any given quantity of a radioactive substance to decay is the half-life of that element. Each particular isotope has its own half-life. For example, the half-life of radium-226 is 1600 years. That is, beginning with 1.00 gram of radium-226, it would take 1600 years for half of it to decay and leave 0.50 gram remaining. After another 1600 years, only 0.25 gram would remain. In each half-life, exactly half of the beginning amount decays.

 Element Isotope Half-life Hydrogen \begin{align*}{^3_1\text{H}}\end{align*} 12.3 years Carbon \begin{align*}{^{14}_{\phantom{0}6} \text{C}}\end{align*} 5730 years Polonium \begin{align*}{^{194}_{\phantom{0}84}\text{Po}}\end{align*} 0.7 seconds Uranium \begin{align*}{^{238}_{\phantom{0}92}\text{U}}\end{align*} 4.5 × 109 years

#### Example

4.00 grams of tritium (hydrogen-3) are produced in the lab. How much of it will remain after 24.6 years?

24.6 years is two half-lives for hydrogen-3, so \begin{align*}\frac{1}{4}\end{align*} of the original amount will remain. That would be 1.00 gram.

### Summary

• In all nuclear reactions, the total of the atomic numbers on the left side of the equation must equal the total of the atomic numbers on the right side of the equation.
• The sum of the mass numbers on the left of the equation must equal the sum of the mass numbers on the right of the equation.
• The breakup of a larger nucleus into two or more smaller nuclei is called fission.
• The joining together of two or more smaller nuclei to form a larger one is called fusion.
• The time required for half of the atoms in any given quantity of a radioactive substance to decay is the half-life of that element.

### Review

1. The isotope \begin{align*}^{238}_{\phantom{0}93} \text{Np}\end{align*} has a half-life of 2.0 days. If 4.00 grams are produced at noon on Monday, what will be the mass of neptunium remaining at noon on Tuesday of the following week?
2. Write the equation for the alpha decay of a polonium-214 nucleus. Recall from the concept “Radioactivity” that \begin{align*}\alpha \ = \ ^{4}_{2} \text{He}\end{align*}.
3. Complete the following equation: \begin{align*}{^2_1 \text{H}}+{^2_1 \text{H}} \rightarrow {^3_1 \text{H}}+\underline{\hspace{0.5cm}}\end{align*}

### Explore More

Use this resource to answer the questions that follow.

1. What was used as a target in the Cockcroft and Walton experiment?
2. Name two famous scientists whose actual voices are heard in this video.

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