Decay Equations (OCR GCSE Physics A (Gateway))
Revision Note
Writing Decay Equations
Nuclear radioactive decay equations show the changes in mass and charge of the nuclei in the decay
Nuclear equations, just like chemical equations, balance:
The sum of the mass numbers on the left of each equation should equal the sum on the right
The sum of the atomic numbers should also balance on the left and right
The parent nucleus is the nucleus that decays
Subsequently, the daughter nucleus remaining after the decay
Alpha Decay Equation
In nuclear equations representing alpha decay:
The mass number of the daughter nucleus is 4 less than the parent
The atomic number of the daughter nucleus is 2 less than the parent
Alpha decay equation
The following equation shows Polonium-212 undergoing alpha decay
It forms Lead-208 and an alpha particle
An alpha particle can also be written as a helium nucleus (Symbol He)
The polonium nucleus emits an alpha particle, causing its mass and charge to decrease. This means it changes into a new element
Beta Minus Decay Equation
In nuclear equations representing beta minus decay:
The mass number of the daughter nucleus is the same as the parent
The atomic number of the daughter nucleus is 1 more than the parent
Beta-minus decay equation
The following equation shows carbon-14 undergoing beta decay
It forms nitrogen-14 and a beta particle
Beta particles are written as an electron in this equation
The carbon nucleus emits a beta particle, causing its charge to increase. This means it changes into a new element, Nitrogen
Gamma Decay Equation
In nuclear equations representing gamma decay:
The mass number of the daughter nucleus is the same as the parent
The atomic number of the daughter nucleus is the same as the parent
Gamma decay equation
Here is an example of Uranium-238 undergoing gamma decay
Notice that the mass number and atomic number of the unstable nuclei remains the same during the decay
Although the Uranium nucleus is unchanged in structure, its energy reduces during gamma decay
Balancing Decay Equations
Worked Example
A nucleus with 84 protons and 126 neutrons undergoes alpha decay. It forms lead, which has the element symbol Pb.
Which of the isotopes of lead pictured is the correct one formed during the decay?
Answer: A
Step 1: Calculate the mass number of the original nucleus
The mass number is equal to the number of protons plus the number of neutrons
The original nucleus has 84 protons and 126 neutrons
84 + 126 = 210
The mass number of the original nucleus is 210
Step 2: Calculate the new atomic number
The alpha particle emitted is made of two protons and two neutrons
Protons have an atomic number of 1, and neutrons have an atomic number of 0
Removing two protons and two neutrons will reduce the atomic number by 2
84 – 2 = 82
The new nucleus has an atomic number of 82
Step 3: Calculate the new mass number
Protons and neutrons both have a mass number of 1
Removing two protons and two neutrons will reduce the mass number by 4
210 – 4 = 206
The new nucleus has a mass number of 206
Worked Example
A nucleus with 11 protons and 13 neutrons undergoes beta decay. It forms magnesium, which has the element symbol Mg.
Which is the correct isotope of magnesium formed during the decay?
Answer: D
Step 1: Calculate the mass number of the original nucleus
The mass number is equal to the number of protons plus the number of neutrons
The original nucleus has 11 protons and 13 neutrons
11 + 13 = 24
The mass number of the original nucleus is 24
Step 2: Calculate the new atomic number
During beta decay a neutron changes into a proton and an electron
The electron is emitted as a beta particle
The neutron has an atomic number of 0 and the proton has an atomic number of 1
So the atomic number increases by 1
11 + 1 = 12
The new nucleus has an atomic number of 12
Step 3: Calculate the new mass number
Protons and neutrons both have a mass number of 1
Changing a neutron to a proton will not affect the mass number
The new nucleus has a mass number of 24 (the same as before)
Examiner Tips and Tricks
It is easy to forget that an alpha particle is a helium nucleus. The two are interchangeable, so don’t be surprised to see either used in the exam. You are not expected to know the names of the elements produced during radioactive decays, but you do need to be able to calculate the mass and atomic numbers by making sure they are balanced on either side of the reaction.
There is a second form of beta decay during which a proton changes into a neutron. This is called beta-plus decay - you might come across it while revising, but you don't need to know about it for your exam.
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