Beta Decay

Definition of Beta Decay

Beta decay is a type of radioactive decay where an unstable atomic nucleus emits a beta particle. There are two types of beta decay:

• Beta minus (β⁻) decay: emission of an electron
• Beta plus (β⁺) decay: emission of a positron (the electron’s antiparticle)

Beta decay occurs in unstable nuclei that have too many neutrons or protons, helping the nucleus become more stable by changing one type of nucleon into another.

Beta Minus Decay

In beta minus decay, a neutron inside the nucleus changes into a proton. This process emits an electron (called a beta particle) and an antineutrino (a very small, neutral particle).

The key points are:

• A neutron turns into a proton
• An electron (β⁻ particle) is emitted from the nucleus
• An antineutrino is also emitted
• The atomic number increases by 1 because there is one more proton
• The mass number stays the same because a neutron is replaced by a proton

This changes the element into a different one because the proton number defines the element.

For example, carbon-14 undergoes beta minus decay:

Carbon-14 has 6 protons and 8 neutrons (mass number 14). When a neutron changes to a proton, the new nucleus has 7 protons and 7 neutrons, becoming nitrogen-14.

The nuclear equation is:

$_{6}^{14}\text{C} \rightarrow _{7}^{14}\text{N} + \beta^- + \bar{\nu}_e$

Here, $\beta^-$ is the emitted electron and $\bar{\nu}_e$ is the antineutrino.

Beta Plus Decay (Positron Emission)

In beta plus decay, a proton in the nucleus changes into a neutron. This emits a positron (a particle like an electron but with a positive charge) and a neutrino.

Key points:

• A proton turns into a neutron
• A positron (β⁺ particle) is emitted
• A neutrino is emitted
• The atomic number decreases by 1 because there is one less proton
• The mass number remains unchanged

This also transforms the element into a different one by changing the proton number.

For example, carbon-11 undergoes beta plus decay:

Carbon-11 has 6 protons and 5 neutrons. When a proton changes into a neutron, the new nucleus has 5 protons and 6 neutrons, becoming boron-11.

The nuclear equation is:

$_{6}^{11}\text{C} \rightarrow _{5}^{11}\text{B} + \beta^+ + \nu_e$

Here, $\beta^+$ is the emitted positron and $\nu_e$ is the neutrino.

Effects on the Nucleus

Beta decay changes the nucleus in the following ways:

• Proton number changes: In beta minus decay, it increases by 1; in beta plus decay, it decreases by 1.
• Mass number stays the same: Because a neutron and proton have almost the same mass, the total nucleon count doesn’t change.
• Element changes: The change in proton number means the atom becomes a different element.
• Energy is released: The decay releases energy carried away by the emitted particles and radiation.

This process helps unstable nuclei move towards a more stable balance of protons and neutrons.

For example, in beta minus decay of carbon-14, the element changes from carbon to nitrogen, which is more stable.

The emitted beta particle (electron or positron) can be detected and is a form of ionising radiation.

The neutrinos and antineutrinos carry away some energy and momentum but rarely interact with matter, making them very hard to detect. They are emitted to conserve energy, momentum, and angular momentum in the decay process.

Beta decay is important in nuclear medicine, carbon dating, and understanding nuclear reactions. For example, beta emitters are used in radiotherapy to treat cancer.

For instance, beta minus decay is used in carbon dating to estimate the age of archaeological samples by measuring the amount of carbon-14 remaining.

The energy released during beta decay also contributes to the heat inside stars and radioactive rocks.

Remember, beta decay only changes one nucleon type at a time, keeping the total nucleons constant but altering the proton count.

For example, if a nucleus has atomic number $Z$ and mass number $A$, after beta minus decay:

$_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + \beta^- + \bar{\nu}_e$

After beta plus decay:

$_{Z}^{A}X \rightarrow _{Z-1}^{A}Y + \beta^+ + \nu_e$

This notation shows the element $X$ changing into element $Y$ by changing the proton number.

For instance, if potassium-40 undergoes beta minus decay:

Potassium-40 has 19 protons and 21 neutrons. After decay, it becomes calcium-40 with 20 protons and 20 neutrons.

The equation is:

$_{19}^{40}\text{K} \rightarrow _{20}^{40}\text{Ca} + \beta^- + \bar{\nu}_e$

This changes the element from potassium to calcium.

For example, if sodium-22 undergoes beta plus decay:

Sodium-22 has 11 protons and 11 neutrons. After decay, it becomes neon-22 with 10 protons and 12 neutrons.

The equation is:

$_{11}^{22}\text{Na} \rightarrow _{10}^{22}\text{Ne} + \beta^+ + \nu_e$