Calculate the integrated activity in the first seven days

Question

1. Given the total body retention function for chemical element "B",

R = [0.1e^-k₁t + 0.3 e^-k₂t- + 0.6e^-k₃t],

calculate the integrated activity in the first seven days following an intake of 25 MBq of ¹²³B. The radionuclide has a decay constant of 0.04 c1-1 and the coefficients k₁, k₂, and k₃ have values of 0.1 d^-1, 0.05 d^-1, and 0.02 d^-1, respectively.

2. It is usually assumed that alpha emitters don't deposit energy into neighboring tissues. Let's see if it is true. Assume that the kidney is a sphere of unit density (1 g/cm³) with a radius of 5 cm.

Given that this kidney is uniformly contaminated with a radionuclide that emits 5 mev alpha particles {assume a range of 20 microns in the kidney), estimate the fractional alpha energy loss from the kidney due to decays occurring at its edge, Make whatever simplifying assumptions you'd like in order to come up with a reasonable estimate.

3. Using the table of ^99mTc emissions and the table of SAF values (both provided below), calculate the SEE for the liver (source & target; m_t = 1800 g). Hint: you may not need all the information on this table; and the word for the day ... "significance".

Table 2 Partial Listing of the Radiations Emitted by Tc-99m and Their Ai Values
Particles/Transition		Energy/Particle	linergy/Transition
Radiation*                                        (n)		(Et[MeV])	(Δ, [g-rad/μCi-h I) )    Δ[kg-Gy/Bq-s] )t
Gamma i	0.0000	0.0021	0.0000	0.0000
ce-M, gamma 1	0.9160	0.0017	0.0035	2.56E-16
Gamma 2	0.8910	0.1405	0.2670	2.00E-14
ce-K, gamma 2	0.0884	0.1195	0.0225	1.70E-15
ce-I, gamma 2	0.0097	0.1375	0.0029	2.15E-16
ce-M, gamma 2	0.0019	0.1401	0.0006	4.36E-17
ce-K, gamma 3	0.0055	0.1216	0.0014	1.08E-16
cc-I., gamma 3	0.0017	0.1400	0.0005	2.08E-17
ee-M, gamma 3	0.0034	0.1422	0.0001	7.64E-18
K alpha-1 x ray	0.0399	0.0184	0.0016	1.17E-16
K alpha-2 x ray	0.0210	0.0183	0.0008	6.14E-17
K. beta-1 x ray	0.0068	0.0206	0.0003	2.26E-17
E.I.I. auger electrons	0.0139	0.0763	0.0005	3.42E-17
MA auger electrons	0.0057	0.0533	0.0002	1.63E-17
1.1\4N1 auger electrons	0.0679	0.0041	0.0003	2.22E-17
NIXY auger electrons	1.1100	0.0004	0.0010	7.27E-17
*ce = conversion electrons.
Digits after the symbol 1 indicate the power of 10 by which each number is to be multiplied.