Nuclear Equation

Key Stage 4

Meaning

A nuclear equation is a type of symbol equation used to show the changes which take place in a radioactive decay.

About Nuclear Equations

Nuclear equations can be used to predict the products of a radioactive decay or a series of decays which take place one after the other.

In nuclear equations the relative atomic mass and relative atomic charge accompany the symbols for the elements and the ionising radiation they produce.

General Formulae

Alpha Decay

\({}_Z^AX \rightarrow {}_{Z-2}^{A-4}Y + {}_2^4\alpha\)

Beta Decay

\({}_Z^AX \rightarrow {}_{Z+1}^{A}Y + {}_{-1}^0\beta\)

Gamma Emission

\({}_Z^AX \rightarrow {}_Z^AX + {}_0^0\gamma\)

Neutron Decay

\({}_Z^AX \rightarrow {}_{Z}^{A-1}Y + {}_0^1n\)

Examples

Alpha Decay

\({}_{92}^{238}U \rightarrow {}_{90}^{234}Th + {}_2^4\alpha\)

Beta Decay

\({}_{28}^{65}Ni \rightarrow {}_{29}^{65}Cu + {}_{-1}^0\beta\)

Gamma Decay

\({}_{42}^{99}Mo \rightarrow {}_{42}^{99}Mo + {}_0^0\gamma\)

Neutron Decay

\({}_{8}^{18}O \rightarrow {}_{8}^{17}O + {}_0^1n\)

Induced Nuclear Fission

\({}_{92}^{235}U + {}_{0}^{1}n \rightarrow {}_{92}^{236}U \rightarrow {}_{36}^{85}Kr + {}_{56}^{148}Ba + 3{}_{0}^{1}n\)

Nuclear Fusion

\({}_1^2H + {}_1^3H \rightarrow {}_2^4He + {}_0^1n\)

Calculating the Element/Isotope

Alpha Decay
Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{84}^{210}Po \rightarrow {}_{Z}^{A}X + {}_2^4\alpha\)	Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{Z}^{A}X \rightarrow {}_{86}^{222}Rn + {}_2^4\alpha\)
1. Calculate the relative atomic mass by looking at the top row of numbers. 210 = A + 4 A = 206	1. Calculate the relative atomic mass by looking at the top row of numbers. A = 222 + 4 A = 226
2. Calculate the relative atomic charge by looking at the bottom row of numbers. 84 = Z + 2 Z = 82	2. Calculate the relative atomic charge by looking at the bottom row of numbers. Z = 86 + 2 Z = 88
3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{82}^{206}Pb\)	3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{88}^{226}Ra\)

Beta Decay
Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{7}^{13}N \rightarrow {}_{Z}^{A}X + {}_{-1}^0\beta\)	Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{Z}^{A}X \rightarrow {}_{48}^{111}Cd + {}_{-1}^0\beta\)
1. Calculate the relative atomic mass by looking at the top row of numbers. 13 = A + 0 A = 13	1. Calculate the relative atomic mass by looking at the top row of numbers. A = 111 + 0 A = 111
2. Calculate the relative atomic charge by looking at the bottom row of numbers. 7 = Z - 1 Z = 8	2. Calculate the relative atomic charge by looking at the bottom row of numbers. Z = 48 - 1 Z = 47
3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{8}^{13}O\)	3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{47}^{111}Ag\)

Gamma Emission
Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{90}^{231}Th \rightarrow {}_{Z}^{A}X + {}_0^0\gamma\)	Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{Z}^{A}X \rightarrow {}_{77}^{192}Ir + {}_0^0\gamma\)
1. Calculate the relative atomic mass by looking at the top row of numbers. 231 = A + 0 A = 231	1. Calculate the relative atomic mass by looking at the top row of numbers. A = 192 + 0 A = 192
2. Calculate the relative atomic charge by looking at the bottom row of numbers. 90 = Z + 0 Z = 90	2. Calculate the relative atomic charge by looking at the bottom row of numbers. Z = 77 + 0 Z = 77
3. It's the same element. \({}_{90}^{231}Th\)	3. It's the same element. \({}_{77}^{192}Ir\)

Neutron Decay
Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{3}^{8}Li \rightarrow {}_{Z}^{A}X + {}_0^1n\)	Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{Z}^{A}X \rightarrow {}_{10}^{26}Ne + {}_0^1n\)
1. Calculate the relative atomic mass by looking at the top row of numbers. 8 = A + 1 A = 7	1. Calculate the relative atomic mass by looking at the top row of numbers. A = 26 + 1 A = 27
2. Calculate the relative atomic charge by looking at the bottom row of numbers. 3 = Z + 0 Z = 3	2. Calculate the relative atomic charge by looking at the bottom row of numbers. Z = 10 + 0 Z = 10
3. It's the same element but a different isotope. \({}_{3}^{7}Li\)	3. It's the same element but a different isotope. \({}_{10}^{27}Ne\)

Calculating Fission Products

Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \( {}_{92}^{236}U \rightarrow {}_{53}^{131}I + {}_{Z}^{A}X + 3{}_{0}^{1}n\)	Find the element 'X' and calculate its relative atomic mass 'A' and its relative atomic charge 'Z'. \({}_{92}^{236}U \rightarrow {}_{38}^{90}Sr + {}_{Z}^{A}X + 2{}_{0}^{1}n\)
1. Calculate the relative atomic mass by looking at the top row of numbers. 236 = 131 + A + 3 A = 236 - 134 A = 102	1. Calculate the relative atomic mass by looking at the top row of numbers. 236 = 90 + A + 2 A = 236 - 92 A = 144
2. Calculate the relative atomic charge by looking at the bottom row of numbers. 92 = 53 + Z + 0 Z = 39	2. Calculate the relative atomic charge by looking at the bottom row of numbers. 92 = 38 + Z + 0 Z = 54
3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{39}^{102}Y\)	3. Since the relative atomic charge is the same as the atomic number look up the element on the periodic table. \({}_{54}^{144}Xe\)

References