Solutions 7

For these exercises it might be usfull to have wallet cards they can for instance be found at Nudat 2

1:

1. [math]\frac{m}{M_{m}}\cdot N_{a}\cdot \% = N [/math]
   [math]\frac{N}{\lambda}=D[/math]
   Where m is mass, M_m is molar mass, N_a is avogadros constant, % is the percentage N is the number of atoms λ disintigration constant.
2. Since the half-life of potassium is so low we can assume that the amount lost due to decay is negligible. The amount of potassium is constant
   [math]G=\frac{D\cdot t\cdot E}{m}[/math]
   where G is dose in J/kg, D is the Disintegration rate, t is the time and E is the energy deposited by the radiation.

2:

1. [math]D\cdot\lambda=N[/math]
   [math]\frac{N}{N_{a}}\cdot M_{m}=m[/math]
   
2. First calculate the effective half-life in the body [math]T_{eff}=\frac{T_{Bi}\cdot T_{phy}}{T_{Bi}+T_{phy}}[/math]