﻿ Beta Particles - College Physics

# Beta Particles

## Introduction

Beta particle or $$\beta$$ particle is ionizing radiation that occurs at beta decay.

A distinction is made in the beta radiation between two types, the $$\beta^-$$ particles consisting of electrons and the rare $$\beta^+$$ particles, consisting of positrons.

### Difference to $$\alpha$$ particle

Die emittierten Alphateilchen bei der Alphastrahlung haben eine bestimmte kinetische Energie, die vom Mutternuklid abhängt. Im Gegensatz dazu wird bei dem Betazerfall eines Nuklids Betastrahlung mit ganz unterschiedlicher Energie frei. Die Energie der Betastrahlung reicht dabei von Null bis zu einem für den zerfallenden Kern charakteristischen Maximalwert. Der Grund dafür ist, dass die Energie sich bei dem Betazerfall auf das Betateilchen und ein ebenfalls erzeugtes Neutrino aufteilt. Die Energieverteilung schwankt dabei, sodass die Betateilchen unterschiedliche Energien haben. Die typische maximale Energie von Betastrahlung liegt in der Größenordnung von 1 $$MeV$$.

## $$\beta^+$$ decay

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Nuclides with an excess of neutrons decay by the $$\beta^-$$ process. In this case, the core a neutron is converted into a proton and an electron and an electron-Antineutrino are emitted. Both electron and antineutrino leave the nucleus. However the converted proton is subject to strong interaction and remains in the nucleus.

Since after the decay there is one neutron less but one proton more in the nucleus, the mass number $$\mathrm {A}$$ remains unchanged while the atomic number $$\mathrm{Z}$$ is increased by 1. The element has changed into his successor in the periodic table.

The decay of the neutron can be described by the following formula:

$${}^{1}_{0} \mathrm {n} \to {}^{1}_{1} \mathrm {p} + \mathrm{e}^{-} + \overline{\nu}_e$$

In general the following holds for the $$\beta^-$$ decay:

$${}^\mathrm{A}_\mathrm{Z} \mathrm {X} \to {}^\mathrm{A}_{\mathrm{Z}+1} \mathrm {Y} + \mathrm{e}^{-} \mathrm + \overline{\nu}_e$$

For example the decay of $$\beta^-$$ emitter Au-198:

$${}^{198}_{\ 79} \mathrm {Au} \to {}^{198}_{\ 80} \mathrm {Hg} + \mathrm{e}^{-}+ \overline{\nu}_e$$

The $$\beta^+$$ decay occurs in proton-rich nuclides. In this case, a proton of the nucleus is converted to a neutron and a positron, also an electron and a neutrino is emitted. As with the $$\beta^-$$ decay the mass number remains unchanged, but the atomic number is decreased by 1. The element changes therefore in its predecessor in the periodic table.

The decay of the proton can be described by the following formula:

$${}^{1}_{1} p \to {}^{1}_{0} \mathrm {n} + \mathrm{e}^{+} + \nu_e$$

In general the following holds for the $$\beta^+$$ decay:

$${}^\mathrm{A}_\mathrm{Z} \mathrm {X} \to {}^\mathrm{A}_{\mathrm{Z}-1} \mathrm {Y} + \mathrm{e}^{+} + \nu_e$$

For example the decay of $$\beta^+$$ emitter K-40:

$${}^{40}_{19} \mathrm {K} \to {}^{40}_{18} \mathrm {Ar} + \mathrm{e}^{+} + \nu_e$$

### Electron capture

The so-called electron capture is a competitive process to the $$\beta^+$$ decay. Thereby a proton of the nucleus transforms into a neutron and a neutrino through capture of an electron from the electron shell.

## Decay of the free neutron

Not only neutrons that are in the nucleus, but also free neutrons can decay. They transform into a proton, an antineutrino and an electron which can be detected as beta particle.

The formula for the decay:

$$\hbox{n}\to\hbox{p}+\hbox{e}^-+\overline{\nu}_{\mathrm{e}}$$

Because free neutrons in general have a relatively long life of about 885.7 seconds, however, this does not occur very often. Most free neutrons are captured more quickly by other atomic nuclei.

## Characteristics

When beta particles penetrate into a material, energy is transfered to the material and layers near the surface are ionized, corresponding to the penetration depth of the particles.

### Interaction with matter

Beta particle penetrates paper without problems as opposed to alpha particle. Therefore you need at least a thin aluminum sheet for shielding.

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## Biological effect on humans

### Outside the body

Beta particle penetrates into the skin layers of humans and damages them. This can lead to intense burns and resulting long-term consequences such as skin cancer. In addition, the radiation damages the eyes, it may lead to cataract.

### Inside the body

If beta emitters get into the body as by ingestion or by inhalation, living cells nearby the emitter are damaged. Well documented is thyroid cancer, which is caused by accumulated radioactive iodine-131 in the thyroid.

## Protection against $$\beta$$ particle

In order to protect themselves from beta particle, you can use a few millimeters thick absorber (for example aluminum sheet). These shield the radiation relatively well, but a part of the beta particle is converted into Bremsstrahlung. Therefore you should use shielding material with low atomic number to shield the beta particles. It may be followed then a heavy metal as a second absorber, which shields the Bremsstrahlung.

Material dependant maximum reach for $$\beta$$-particles:

Nuclide Energy Air Plexiglas Glass
$${}^{3}_{ } H$$ 19 $$keV$$ 8 $$cm$$ - -
$${}^{14}_{ } C$$ 156 $$keV$$ 65 $$cm$$ - -
$${}^{35}_{ } S$$ 167 $$keV$$ 70 $$cm$$ - -
$${}^{131}_{ } I$$ 600 $$keV$$ 250 $$cm$$ 2,6 $$mm$$ -
$${}^{32}_{ } P$$ 1710 $$keV$$ 710 $$cm$$ 7,1 $$mm$$ 4,0 $$mm$$

### Sources

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