IB Physics Topic E.3.2 Types of Radioactive Decay Revision Notes (SL/HL)

IB Physics Topic E.3.2 Types of Radioactive Decay Revision Notes (SL/HL) | RevisionDojo

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Alpha Decay: Emission of Helium Nuclei

Definition

Alpha decay

Alpha decay occurs when an unstable nucleus emits an alpha particle, which is essentially a helium nucleus made up of two protons and two neutrons ($^4_2 \text{He}$).

This emission reduces the proton number ($Z$) by 2 and the nucleon number ($A$) by 4, producing a new element.

Example

Consider uranium-235 ($^{235}_{92} \text{U}$), which undergoes alpha decay to form thorium-231 ($^{231}_{90} \text{Th}$): $$
^{235}_{92} \text{U} \rightarrow ^{231}_{90} \text{Th} + ^4_2 \text{He}
$$
Here’s what happens:
- The proton number ($Z$) decreases by 2: $92 \rightarrow 90$.
- The nucleon number ($A$) decreases by 4: $235 \rightarrow 231$.

Energy Released During Alpha Decay

The energy released in alpha decay comes from the mass defect, the difference in mass between the parent nucleus and the products.
Using Einstein's equation, $E = \Delta m c^2$, this energy can be found from the mass difference between the parent nucleus and the products. A full worked calculation is shown in E.3.1.

This energy is carried away as the kinetic energy of the alpha particle and the recoiling daughter nucleus.

Tip

Alpha particles are highly ionizing but have low penetration power.
They can be stopped by a sheet of paper or a few centimeters of air.

Beta Decay: Conversion of Neutrons or Protons

Beta Minus ($\beta^-$) Decay

Definition

Beta minus decay

In beta minus decay, a neutron in the nucleus is converted into a proton, emitting an electron ($\beta^-$) and an antineutrino ($\bar{\nu}$):

$$
n \rightarrow p + e^- + \bar{\nu}
$$

This increases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.

Example

For thorium-234 decay: $$
^{234}_{90} \text{Th} \rightarrow ^{234}_{91} \text{Pa} + e^- + \bar{\nu}
$$
Here:
- The proton number ($Z$) increases by 1: $90 \rightarrow 91$.
- The nucleon number ($A$) remains $234$.

Beta Plus ($\beta^+$) Decay

Definition

Beta plus decay

In beta plus decay, a proton is converted into a neutron, emitting a positron ($\beta^+$) and a neutrino($\nu$):

$$
p \rightarrow n + e^+ + \nu
$$

This decreases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.

Example

Sodium-22 decay:

$$
^{22}_{11} \text{Na} \rightarrow ^{22}_{10} \text{Ne} + e^+ + \nu
$$

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Alpha Decay: Emission of Helium Nuclei

Definition

Alpha decay

Alpha decay occurs when an unstable nucleus emits an alpha particle, which is essentially a helium nucleus made up of two protons and two neutrons ($^4_2 \text{He}$).

This emission reduces the proton number ($Z$) by 2 and the nucleon number ($A$) by 4, producing a new element.

Example

Consider uranium-235 ($^{235}_{92} \text{U}$), which undergoes alpha decay to form thorium-231 ($^{231}_{90} \text{Th}$): $$
^{235}_{92} \text{U} \rightarrow ^{231}_{90} \text{Th} + ^4_2 \text{He}
$$
Here’s what happens:
- The proton number ($Z$) decreases by 2: $92 \rightarrow 90$.
- The nucleon number ($A$) decreases by 4: $235 \rightarrow 231$.

Energy Released During Alpha Decay

The energy released in alpha decay comes from the mass defect, the difference in mass between the parent nucleus and the products.
Using Einstein's equation, $E = \Delta m c^2$, this energy can be found from the mass difference between the parent nucleus and the products. A full worked calculation is shown in E.3.1.

This energy is carried away as the kinetic energy of the alpha particle and the recoiling daughter nucleus.

Tip

Alpha particles are highly ionizing but have low penetration power.
They can be stopped by a sheet of paper or a few centimeters of air.

Beta Decay: Conversion of Neutrons or Protons

Beta Minus ($\beta^-$) Decay

Definition

Beta minus decay

In beta minus decay, a neutron in the nucleus is converted into a proton, emitting an electron ($\beta^-$) and an antineutrino ($\bar{\nu}$):

$$
n \rightarrow p + e^- + \bar{\nu}
$$

This increases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.

Example

For thorium-234 decay: $$
^{234}_{90} \text{Th} \rightarrow ^{234}_{91} \text{Pa} + e^- + \bar{\nu}
$$
Here:
- The proton number ($Z$) increases by 1: $90 \rightarrow 91$.
- The nucleon number ($A$) remains $234$.

Beta Plus ($\beta^+$) Decay

Definition

Beta plus decay

In beta plus decay, a proton is converted into a neutron, emitting a positron ($\beta^+$) and a neutrino($\nu$):

$$
p \rightarrow n + e^+ + \nu
$$

This decreases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.

Example

Sodium-22 decay:

$$
^{22}_{11} \text{Na} \rightarrow ^{22}_{10} \text{Ne} + e^+ + \nu
$$

Definition

Paywall

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics E.3.2 Types of Radioactive Decay Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Alpha Decay: Emission of Helium Nuclei

Energy Released During Alpha Decay

Beta Decay: Conversion of Neutrons or Protons

Beta Minus ($\beta^-$) Decay

Beta Plus ($\beta^+$) Decay

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Alpha Decay: Emission of Helium Nuclei

Energy Released During Alpha Decay

Beta Decay: Conversion of Neutrons or Protons

Beta Minus ($\beta^-$) Decay

Beta Plus ($\beta^+$) Decay

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