# Question bc74d

Jan 23, 2014

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.