Physics 6.18 - 6.22 - Nuclear changes and equations

Physics 6.18 - 6.22 - Nuclear changes and equations

Radioactive decay can change a nucleus into a different element or leave it with less energy. Follow the nucleon changes, then balance nuclear equations using the supplied mass-number and charge data.

Beta decay inside the nucleus

For each decay, take the parent nucleus as the system before the change and the
daughter nucleus as the system after it. Nuclear notation keeps two different counts
visible:

ZAX{}^{A}_{Z}\mathrm{X}
  • AA is the mass number or nucleon number: protons+neutrons\text{protons}+\text{neutrons}.
  • ZZ is the atomic number or proton number: the number of protons. It identifies the element.

Beta-minus decay

In beta-minus decay, a neutron in the nucleus changes into a proton and an electron:

neutron→proton+electron\mathrm{neutron} \rightarrow \mathrm{proton} + \mathrm{electron}

The electron is formed during the nuclear change and leaves as the beta-minus particle. It
is not an electron knocked out of an electron shell. One neutron has become one proton, so
the total number of nucleons is unchanged but the proton number increases by 1:

ZAX→Z+1AY+−10e{}^{A}_{Z}\mathrm{X} \rightarrow {}^{A}_{Z+1}\mathrm{Y} + {}^{0}_{-1}\mathrm{e}

The lower-number balance confirms the direction: Z=(Z+1)+(−1)Z=(Z+1)+(-1).

Beta-plus decay

In beta-plus decay, a proton in the nucleus changes into a neutron and a positron:

proton→neutron+positron\mathrm{proton} \rightarrow \mathrm{neutron} + \mathrm{positron}

A positron is the positive counterpart of an electron; it is not a proton. The positron is
formed and emitted during the decay. One proton has become one neutron, so the total number
of nucleons is unchanged but the proton number decreases by 1:

ZAX→Z−1AY++10e{}^{A}_{Z}\mathrm{X} \rightarrow {}^{A}_{Z-1}\mathrm{Y} + {}^{0}_{+1}\mathrm{e}

Now the lower-number balance is Z=(Z−1)+(+1)Z=(Z-1)+(+1).

These are the process models specified for Combined Science. They provide all the
bookkeeping needed here; the complete particle-physics descriptions contain additional
particles that are outside this lesson's scope.

Do not infer the daughter proton number from the plus or minus sign alone. Follow the nucleon change: neutron to proton means ZZ rises; proton to neutron means ZZ falls.

How emissions change a nucleus

Compare the daughter nucleus with the parent nucleus. If a particle carries nucleons away,
the nucleon count changes. If a proton is lost or a neutron changes into a proton, the
element can change because the proton number identifies the element.

EmissionWhat leaves or changesChange in proton number, ΔZ\Delta ZChange in nucleon number, ΔA\Delta A
alpha, 24He{}^{4}_{2}\mathrm{He}two protons and two neutrons leave together-2-4
beta-minus, −10e{}^{0}_{-1}\mathrm{e}neutron becomes proton; electron leaves+10
beta-plus, +10e{}^{0}_{+1}\mathrm{e}proton becomes neutron; positron leaves-10
gamma, 00γ{}^{0}_{0}\gammaenergy leaves as electromagnetic radiation00
neutron, 01n{}^{1}_{0}\mathrm{n}one neutron leaves0-1

The signs describe the daughter relative to the parent. For example, beta-minus has a
negatively charged emitted particle but makes the daughter's proton number increase.
Neutron emission lowers AA because one nucleon leaves, but it leaves ZZ unchanged
because a neutron carries no charge and is not a proton.

Why gamma radiation can follow another decay

An alpha or beta decay can leave the daughter nucleus in a higher-energy arrangement. The
nucleons then rearrange into a lower-energy arrangement, and the nucleus loses the excess
energy as gamma radiation:

Continue this lesson.

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