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.

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


Radioactive Decay Equations

A= A0 e(-ln2.t / t1/2)

Where:
A = activity now
A0= initial activity
t=time lapsed between now and initial
t1/2= half life of isotope (eg 137Cs = 30.17 yrs, 60Co = 5.27 yrs)

Inputs:

A0:
t:   Year   Month   Day
t1/2:   Year   Month   Day
 
A =

-- OR --

 

A= A0/2n

Where:
A = activity now
A0= initial activity
n = number of half lifes since intial time

Inputs:

A0:
n:
 
A =

Inverse Square Law

I1D12 = I2D22

Where:
I1 = initial intensity (or dose rate)
D1 = initial distance
I2 = new intensity (or dose rate)
D2 = new distance

 

Inputs:

I1:
D1: metres
D2: metres
 
I2 =

 


Half value layer transmission (HVL)

I = I0 / 2n

Where
I = intensity (or dose rate) after shielding
I0= intensity (or dose rate) before shielding
n = number of half value layers

 

Inputs:

I0:
n:
 
I =

Using Transmission Graph

I = I0 x TF

Where:
I = intensity (or dose rate) after shielding
I0= intensity (or dose rate) before shielding
TF = transmission factor as read from graph (ie 0.001)

 

Inputs:

I0:
TF:
 
I =

 


Gamma Factor

Dose rate (H*) = AΓ / D2

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:

A:
Γ:
D: metres
 
H* =

Some typical gamma factors

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

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

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

Prefixes

T = tera = 1012 = 1000 000 000 000
G = giga = 109 = 1000 000 000
M = mega = 106 = 1000 000
k = kilo = 103 = 1000
1 = one = 100 = 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

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