The activity of the contaminant will be 3.5 ×10⁻¹⁰ Bq if the contaminant is 1.1MeV Beta Emitter.
Disclaimer, here the m is taken as 0.5kg.
Given, REM = 1500
Time, t= 1 minute =60 seconds
For beta particles,
RBE (Relative Biological Effectiveness) =2.
Absorbed dose, D =REM/RBE= 1500/2 = 750rad
As 100 rad=1 J/kg,
750 rad=7.5 J/kg
So, D=7.5 J/kg
D= total energy absorbed (E)/mass (m)
7.5 J/kg=E/m
E =7.5 ×0.5 = 3.75J
Therefore, the number of beta particles absorbed is 3.75 J.
The number of beta particles absorbed,
As 1 MeV= 1.6 ×10⁻¹³J
So, converting 1.1 MeV in J, 1.1×1.6 ×10⁻¹³J=1.76×10⁻¹³J
Numbers of beta particles,
n=3.75J/1.76×10⁻¹³J
n=2.13×10⁻¹²
Hence, the number of beta particles is 2.13×10⁻¹².
Activity, A= n/t
where n is the number of beta particles and t is the time.
A= n/t=(2.13×10⁻¹²)/60
A= 3.5 ×10⁻¹⁰ Bq
So, the activity is 3.5 ×10⁻¹⁰ Bq.
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