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3.2.3Interactions with the Environment

Decay Equations

5 min read 9 parts Lesson 12 of 27 Unit quiz

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Section 1 of 9Conservation rules

In any nuclear reaction two quantities are conserved:

Nucleon number
the total nucleon number (mass number, A, the top numbers);
Charge
the total charge (the proton number Z, the bottom numbers).

The sum of the top numbers on the left of the arrow must equal the sum of the top numbers on the right, and the same applies to the bottom numbers. This is the way to check each equation.

Section 2 of 9Alpha decay

An alpha particle is a helium nucleus, 42He (sometimes written 42α). When a nucleus emits an alpha particle its nucleon number falls by 4 and its proton number falls by 2, so it becomes a different element two places earlier in the periodic table. Example:

22688Ra → 22286Rn + 42He

Check226 = 222 + 4 and 88 = 86 + 2.

Section 3 of 9Beta-minus decay

In beta-minus decay a neutron in the nucleus changes into a proton and an electron; the electron is emitted at high speed as the beta particle. The nucleon number stays the same, but the proton number rises by 1, so the element moves one place later. Beta particle: 0−1e. Example:

146C → 147N + 0−1e

Check

  • 14 = 14 + 0 and 6 = 7 + (−1).
  • (A neutral particle called an antineutrino is also emitted;
    • it is usually left out at IGCSE.)

Section 4 of 9Gamma emission

Often a nucleus left over after an alpha or beta emission is in an excited state and gets rid of the excess energy by emitting a gamma ray.

Gamma emission
Gamma emission changes neither the mass number nor the proton number; the nucleus is the same, but at lower energy.
Example: 6027Co → 6028Ni + 0−1e, followed by emission of gamma rays from the excited nickel nucleus.

Section 5 of 9A method for writing equations

1
Write the parent nucleus on the left.
2
Write the emitted particle on the right (He for alpha, e for beta).
3
Subtract the particle's top and bottom numbers from the parent's to get the daughter's numbers.
4
Use the proton number to identify the element from the periodic table.
5
Check the sums on both sides.

Compare decay types in the table below.

DecayChange in AChange in Z
Alpha−4−2
Beta-minus0+1
Gamma00

Section 6 of 9Why the electron comes from the nucleus

It may seem strange that a nucleus without electrons can emit one.

Why the electron comes from the nucleus
In beta-minus decay a neutron changes into a proton, and an electron is created and ejected at the same moment.
The new proton stays in the nucleus, so the proton number rises by one.
Writing the electron as 0−1e shows that the total charge is conserved: the neutron has zero charge, the proton +1 and the electron −1.
  • A decay series can include several alpha and beta decays in turn until a stable nucleus is formed,
    • such as lead-206 at the end of the uranium-238 series.

Section 7 of 9Worked examples

  1. Complete: 23892U → ?Th + 42He.

  2. Strontium-90 (9038Sr) decays by beta-minus emission. Write the equation.

  3. A nucleus of polonium-210 (Z = 84) emits an alpha particle. Find the daughter nucleus.

Section 8 of 9Key terms

TermMeaning
Parent nucleusThe nucleus before decay.
Daughter nucleusThe nucleus formed after decay.
Nucleon numberTotal number of protons and neutrons (top number).
Proton numberNumber of protons (bottom number).

Section 9 of 9Exam technique

1
Forgetting to subtract 2 from the proton number in alpha decay.
2
Changing mass number in beta decay.
3
Writing the electron's lower number as +1.
4
Not checking that top numbers and bottom numbers balance.
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