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# Balancing Nuclear Reactions

## Balancing Nuclear Reactions

A balanced chemical reaction equation reflects the fact that during a chemical reaction, bonds break and form, and atoms are rearranged, but the total numbers of atoms of each element are conserved and do not change. A balanced nuclear reaction equation indicates that there is a rearrangement during a nuclear reaction, but of nucleons (subatomic particles within the atoms’ nuclei) rather than atoms. Nuclear reactions also follow conservation laws, and they are balanced in two ways:

1. The sum of the mass numbers of the reactants equals the sum of the mass numbers of the products.
2. The sum of the charges of the reactants equals the sum of the charges of the products.

If the atomic number and the mass number of all but one of the particles in a nuclear reaction are known, we can identify the particle by balancing the reaction. For instance, we could determine that $${}_{\phantom{\rule{0.5em}{0ex}}8}^{17}\text{O}$$ is a product of the nuclear reaction of $${}_{\phantom{\rule{0.5em}{0ex}}7}^{14}\text{N}$$ and $${}_{2}^{4}\text{He}$$ if we knew that a proton, $${}_{1}^{1}\text{H},$$ was one of the two products. The example below shows how we can identify a nuclide by balancing the nuclear reaction.

## Example

### Balancing Equations for Nuclear Reactions

The reaction of an α particle with magnesium-25 $$({}_{12}^{25}\text{Mg})$$ produces a proton and a nuclide of another element. Identify the new nuclide produced.

### Solution

The nuclear reaction can be written as:

$${}_{12}^{25}\text{Mg}+{}_{2}^{4}\text{He}\;⟶\;{}_{1}^{1}\text{H}+{}_{\text{Z}}^{\text{A}}\text{X}$$

where A is the mass number and Z is the atomic number of the new nuclide, X. Because the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products:

$$25+4=\text{A}+1,\;\text{or A}=28$$

Similarly, the charges must balance, so:

$$12+2=\text{Z}+1,\;\text{and Z}=13$$

Check the periodic table: The element with nuclear charge = +13 is aluminum. Thus, the product is $${}_{13}^{28}\text{Al}.$$

Following are the equations of several nuclear reactions that have important roles in the history of nuclear chemistry:

• The first naturally occurring unstable element that was isolated, polonium, was discovered by the Polish scientist Marie Curie and her husband Pierre in 1898. It decays, emitting α particles:

$${}_{\phantom{\rule{0.5em}{0ex}}84}^{212}\text{Po}\;⟶\;{}_{\phantom{\rule{0.5em}{0ex}}82}^{208}\text{Pb}+{}_{2}^{4}\text{He}$$

• The first nuclide to be prepared by artificial means was an isotope of oxygen, 17O. It was made by Ernest Rutherford in 1919 by bombarding nitrogen atoms with α particles:

$${}_{\phantom{\rule{0.5em}{0ex}}7}^{14}\text{N}+{}_{2}^{4}\text{He}\;⟶\;{}_{\phantom{\rule{0.5em}{0ex}}8}^{17}\text{O}+{}_{1}^{1}\text{H}$$

• James Chadwick discovered the neutron in 1932, as a previously unknown neutral particle produced along with 12C by the nuclear reaction between 9Be and 4He:

$${}_{4}^{9}\text{Be}+{}_{2}^{4}\text{He}\;⟶\;{}_{\phantom{\rule{0.5em}{0ex}}6}^{12}\text{C}+{}_{0}^{1}\text{n}$$

• The first element to be prepared that does not occur naturally on the earth, technetium, was created by bombardment of molybdenum by deuterons (heavy hydrogen, $${}_{1}^{2}\text{H})$$, by Emilio Segre and Carlo Perrier in 1937:

$${}_{1}^{2}\text{H}+{}_{42}^{97}\text{Mo}\;⟶\;2{}_{0}^{1}\text{n}+{}_{43}^{97}\text{Tc}$$

• The first controlled nuclear chain reaction was carried out in a reactor at the University of Chicago in 1942. One of the many reactions involved was:

$${}_{\phantom{\rule{0.5em}{0ex}}92}^{235}\text{U}+{}_{0}^{1}\text{n}\;⟶\;{}_{35}^{87}\text{Br}+{}_{\phantom{\rule{0.5em}{0ex}}57}^{146}\text{La}+3{}_{0}^{1}\text{n}$$