Handout: Writing and balancing nuclear equations

The number of nucleons and the total electric charge are conserved in simple nuclear reactions. If the mass number and atomic numbers of the particles emitted from a nucleus are known, the product nucleus can be identified by balancing mass numbers and atomic numbers in the nuclear equation.

Procedure

Step 1. Identify the type of particle emitted by the decay and write the nuclear equation, with the mass number and the atomic number of the daughter nucleus written as A and Z, respectively.

Step 2. Find the values of A and Z for the daughter nucleus from the requirement that the sums of the mass numbers and the nuclear charges remain unchanged in the decay.

Step 3. Use A and Z to identify the daughter nucleus in the periodic table.

The masses and charges of the most common particles ejected or captured by nuclei are as follows:

Particle emitted

 Mass number Charge Examples
alpha, a (helium nucleus) 4 2 21184Po ---> 20782Pb + 42He
beta, b (electron) 0 -1 2411Na ---> 2412Mg + 0-1e
gamma, g (light energy) 0 0 9943Tc ---> 9943Tc + g

 

EXAMPLE 1 Writing a nuclear equation for a decay

Write the nuclear equation for the a decay of thorium-232.

STRATEGY The total number of nucleons (mass number) and total charge must be the same on each side of the equation. An a particle has a charge of +2 and a mass number of 4, so emission of an a particle decreases the atomic number by 2 and the mass number by 4.

SOLUTION Write the equation with AZE representing the daughter nucleus:

23290Th ---> AZE + 42a

To balance mass, we find from 232 = A + 4 that A = 228. To balance charge, Z must equal 90 - 2 = 88, so the daughter nucleus is 22888Ra. The balanced nuclear equation is

23290Th ---> 22888Ra + 42a

SELF-TEST 1 Write the nuclear equation for (a) the a decay of plutonium-242 and (b) positron emission by sodium-22

[Answer: (a) 24294Pu ---> 23892U + 42a; (b) 2211Na ---> 2210Ne + b+]

 

EXAMPLE 2 Writing a nuclear equation for b decay

Write the nuclear equation for the b decay of lithium-9.

STRATEGY The total number of nucleons (mass number) and total charge must be the same on each side of the equation to determine the identity of the isotope required to balance the equation. A b particle has a charge of -1 and zero mass number, so emission of a b particle increases the atomic number by 1, but leaves the mass number unchanged.

SOLUTION Write the equation with AZE representing the daughter nucleus:

93Li ---> AZE + 0-1e

To balance mass, we find from 9 = A + 0 that A = 9. To balance charge, Z must equal 3 - (-1) = 4, so the daughter nucleus is 94Be. The balanced nuclear equation is

93Li ---> 94Be + 0-1e

SELF-TEST 2 Write the nuclear equation for b decay of indium-115.

[Answer: 11549In ---> 11550Sn + 0-1e]

 

 

This handout is a modification of text being prepared for publication in Chemistry: Molecules, Matter and Change, 4th edition, by L. Jones and P. Atkins, W. H. Freeman and Co.