# Why must nuclear equations must be balanced?

May 9, 2014

Nuclear equations must be balanced because they must obey the law of conservation of mass and the law of conservation of charge.

In a nuclear symbol such as $\text{_1^2"H}$, the 1 is the atomic number — the number of protons. It also represents the charge, since the charge on a proton is +1.

The 2 is the mass number — the number of protons and neutrons.

That means that the sum of all the subscripts (charges) and of all the superscripts (masses) must be the same on each side of the equation.

Let's see how this works in some typical nuclear reactions.

α Decay

$\text{_92^234"U" → _90^230"Th" + _2^4"He}$

β⁻ Decay

$\text{_92^233"U" → _93^233"Np" + _-1^0"e}$

β⁺ Decay

$\text{_12^23"Mg" → _11^23"Na" + _1^0"e}$

Fission

$\text{_92^235"U" + _0^1"n" → _57^146"La" + _35^87"Br" + 3_0^1"n}$

Fusion

$\text{_1^2"H" + _1^2"H" → _2^4"He}$

In all cases, the sum of the subscripts (charges) and the sum of the superscripts (masses) is the same on each side of the equation.