# Nuclear Equations

Nuclear Equations - Explained

Tip: This isn't the place to ask a question because the teacher can't reply.

## Key Questions

• Nuclear equations represent the reactants and products in radioactive decay, nuclear fission, or nuclear fusion.

Instead of chemical equations where it shows the different number of elements is conserved in a reaction, in a nuclear reaction the atomic mass and proton number are conserved.

In these examples the sum of the masses (top) and the sum of the proton numbers (bottom) are the same on both sides:

${\text{_3^6Li+""_1^2H>2}}_{2}^{4} \alpha$

As you can see the elements haven't been conserved, but the mass number and proton number have $6 + 2 = 2 \cdot 4$, and $3 + 1 = 2 \cdot 2$

Another example:
${\text{_6^(14)C>""_7^(14)N+}}_{- 1}^{0} \beta$

Again, in this equation, the elements haven't been conserved, by the mass number and proton number have $14 = 14 + 0$, and $6 = 7 - 1$

You balance nuclear equations by making the sum of the superscripts and the sum of the subscripts the same on each side of the equation.

#### Explanation:

The symbol for a nucleus is $\text{_Z^A"X}$.

The number at the upper left is the mass number, $A$. It identifies the number of protons and neutrons in the nucleus.

The number at the lower left is the atomic number, $Z$. It identifies the element $\text{X}$. Thus, the symbol for uranium-238 is $\text{_92^238"U}$.

We use special symbols for α and β particles and for protons and neutrons:

α = ""_2^4"He"; β =color(white)(l)_text(-1)^0"e"; proton = $\text{_1^1"H}$; neutron = $\text{_0^1"n}$

In a balanced nuclear equation, the sums of the superscripts and the sums of the subscripts must be equal on each side of the equation.

EXAMPLE

Write an equation for the decay of calcium-45 to scandium-45.

Solution

Complete the unbalanced equation.

$\text{_20^45"Ca" → _21^45"Sc}$ + ?

The missing particle must have $Z$ = 20 - 21 = -1 and $A$ = 45 - 45 = 0.

The missing particle is ${\textcolor{w h i t e}{l}}_{\textrm{- 1}}^{0} \text{e}$ (a β particle or electron), so the equation is

$\text{_20^45"Ca" → _21^45"Sc" + color(white)(l) _text(-1)^0"e}$

Here's a useful video on balancing nuclear equations.

• First some definitions:
A. Isotopes - atoms with the same number of protons, but a different number of neutrons (same element, different isotopic mass).
Carbon can exist the isotopes carbon-12, carbon-13, and carbon-14. They both have 6 protons (or else they wouldn't be carbon), but a different number of neutrons.
C-12 has 6 protons and 6 neutrons
C-13 has 6 protons and 7 neutrons
C-14 has 6 protons and 8 neutrons

B. Radioactive nucleus - a nucleus that spontaneously changes and emits (releases) energy. This occurs spontaneously: by itself and with no outside energy required. Many isotopes do it naturally.
All nuclei with more than 84 protons (Polonium and up) are radioactive. As well as those with with more neutrons than protons Carbon-14 is radioactive

Balancing: The sum of the isotopic masses (top numbers) are equal on both sides of the equation.
The sum of the atomic numbers (the bottom numbers) also are equal on both sides of the equation.

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