** Useful equations**

** Fixed Industrial Gauges Course **

The following are equations that may be used for the calculation of fundamental values for use with fixed industrial radiation gauges. Also at the base of the page is a list of common prefixes.

- Radioactive decay equations
- Inverse Square Law
- Half Value Layers (HVL)
- Transmission
- Specific Gamma Ray Emission Factor (Gamma Factor)
- Prefixes

If a result is given as **NaN** then check the values you entered as one must be incorrrect/invalid

## Radioactive Decay Equations

A= A_{0} e^{(-ln2.t / t1/2)}

Where:

A = activity now

A_{0}= initial activity

t=time lapsed between now and initial

t_{1/2}= half life of isotope (eg ^{137}Cs = 30.17 yrs, ^{60}Co = 5.27 yrs)

**Inputs:**

## -- OR --

A= A_{0}/2^{n}

Where:

A = activity now

A_{0}= initial activity

n = number of half lifes since intial time

**Inputs:**

## Inverse Square Law

I_{1}D_{1}^{2} = I_{2}D_{2}^{2}

Where:

I_{1} = initial intensity (or dose rate)

D_{1} = initial distance

I_{2} = new intensity (or dose rate)

D_{2} = new distance

**Inputs:**

## Half value layer transmission (HVL)

I = I_{0} / 2^{n}

Where

I = intensity (or dose rate) after shielding

I_{0}= intensity (or dose rate) before shielding

n = number of half value layers

**Inputs:**

## Using Transmission Graph

I = I_{0} x TF

Where:

I = intensity (or dose rate) after shielding

I_{0}= intensity (or dose rate) before shielding

TF = transmission factor as read from graph (ie 0.001)

**Inputs:**

## Gamma Factor

Dose rate (H_{*}) = AΓ / D^{2}

Where:

H_{*} = dose rate in μ Sv/h

A = activity in MBq (or GBq)

Γ = gamma factor from 1 MBq (or GBq) at 1m

D = distance in metres

NOTE: do not mix MBq and GBq references in the same equation

**Inputs:**

## Some typical gamma factors

**Γ** for ^{137}Cs-: 90μSv/h from 1 GBq at 1m **-or-** 0.090 μSv/h from 1MBq at 1m

**Γ** for ^{60}Co-: 315μSv/h from 1 GBq at 1m **-or-** 0.315 μSv/h from 1MBq at 1m

**Γ** for ^{192}Ir-: 130μSv/h from 1 GBq at 1m **-or-** 0.130 μSv/h from 1MBq at 1m

## Prefixes

T | = tera | = 10^{12} |
= 1000 000 000 000 |

G | = giga | = 10^{9} |
= 1000 000 000 |

M | = mega | = 10^{6} |
= 1000 000 |

k | = kilo | = 10^{3} |
= 1000 |

1 | = one | = 10^{0} |
= 1 |

m | = milli | = 10^{-3} |
= 0.001 |

μ | = micro | = 10^{-6} |
= 0.000 001 |

n | = nano | = 10^{-9} |
= 0.000 000 001 |

‘Rule of thumb’ –

- converting big to small unit (ie M to k), move the decimal place to the RIGHT.

- converting small to big unit (ie M to G), move the decimal place to the LEFT