# Radiation Attenuation over Different Materials

## Contents

# Description of the Experiment

This laboratory uses a Geiger-Müller detector to measure the radiation from a radioactive source (\( ^{241}Am_{95} \), Amerício), and study, by putting diferent materials between the source and the detector, the absorption of radiation of said materials.

# Experimental Apparatus

The user can set the distance between source and detector (between 6cm and 20cm), and choose which material to position between the two parts.

The avaliable material are:

Position | Material | Thickness |
---|---|---|

1 | Wood | 10 mm |

2 | Corticite | 10 mm |

3 | Brick | 10 mm |

4 | Copper | 0,2 mm |

5 | Copper | 0,4 mm |

6 | Copper | 0,8 mm |

7 | Copper | 1,6 mm |

8 | Copper | 3,2 mm |

9 | Control window (air) | 0,5 mm |

10 | Lead | 6 mm |

The tenth position is, actually, "closing" the source.

# Protocol (Basic Laboratory)

The suggested protocol for this experiment in the Basic Laboratory is the following:

- Study the variation of the radiation's intensity as the distance changes, given by the detector's output;
- Verify the linear absorption rate of the diferent materials, trying to establish a theoretical law that relates the in intensity with the surface mass of each element;
- For copper, infer lengh of semi-reduction, i.e. the lengh it takes to halve the number of Geiger-Müller counts;
- The user will observe that experiments conducted in the same condition will give diferent values. This is caused by the randomness of nuclear processes. A way to prove this is to verify that the number of counts in the same condition follow a Binomial or Poisson Distribution due to extremelly low probability of the event.

Because of this last factor, the experimental error can be atenuated by adding several values of radioactive decay in the same conditions.

# Advanced Protocol (Intermidiate Laboratory)

A slightly more advanced protocol is:

- Looking at Americium's (\(^{241}Am_{95}\)) half-life and at the database, compare the number of decays in the same conditions (material in between and distance) in the past and in the present.
- Verify the mathematical law for Radioactive Decay.
- For the same material and distance, record a large number of decays.
- Fit a Gaussian function to the data and see if, by adding more experimental data, the fitting improves.

# Data Analysis

Under construction.

# Theoretical Principles

## Geiger-Müller Detector

This device detects radiation levels, providing a number corresponding to how many radioactive particles go through it.

## Radioactive Decay

The mathematical law that describes radioactive decay tells us that the variation of the number of radioactive nuclei, i.e. the number of decays at a given instant, is proportional to it's quantity:

\[ \frac{dN}{dt} = - \lambda \times N \]

where \( \lambda \) is the decay constant. The solution of this equation tells us that, for a given time, the number of remaining nuclei is \[ N = N_0 \times e^{- \lambda t} \]

Differentiating with respect to time, we get the sample's rate of decay (i.e. how many decays occur per second) a.k.a. radioactivity. \[ R = \frac{dN}{dt} = N_0 \times \lambda \times e^{- \lambda t} \]

The half-life, as the name implies, is the time it takes for an inicial sample to decay into half: \[ T_{^1/_2} = \frac{ln(2)}{\lambda} \]