Radioisotopes can be used in medical diagnosis and therapy as well as industrial analysis. Many radi — Physical Chemistry — Kinetics Chemistry Question
Preparation and Applications of Radioisotopes
Radioisotopes can be used in medical diagnosis and therapy as well as industrial analysis. Many radioisotopes, e.g. 32 P (Mass number = 32) and 60 Co can be generated by the irradiation of neutrons in a nuclear reactor. However, some radioisotopes in nature, e.g. 14 C and 3 T (tritium), can be produced by the bombardment of nitrogen 14 N atoms in the atmosphere by neutrons in the cosmic ray. (Atomic numbers of T & H, C, N, P, Co and neutron are 1, 6, 7, 15, 27 and 0, respectively. 32 P can be denoted as 32 15P ).
Radioisotope 14 C can be used as a reagent in 14 C dating. The activity (A) in terms of counts per minute (cpm) of the radioisotope 14 C is proportional to the number (N) of 14 C atoms as follows : [ 14 C Dating]
A = ε λ N (1)
where ε is the detection coefficient of a detector for 14 C and λ is the decay constant of 14 C.
An initial amount (No) of 14 C can be reduced to the amount (N) of 14 C by decay after a given time (t) as follows:
N = No e –t
(2)
The half life (t1/2) of 14 C is 5730 years which is defined as the time required for 50 % of the number of the radioisotope 14 C atoms in a sample to undergo decay, that is N = 1/2 No. It is well known that activity (Ao) of 14 C in a living animal or plant is kept to be around 16.5 cpm/g of carbon. After the death of the animal or plant, the activity (cpm/g of carbon) of 14 C in the body of the living animal or plant is decreased by the time passed.
The radioisotope 32 P is a very important leveling reagent for biological research and can be produced by the bombardment of 31 P by a neutron in a nuclear reactor. The production rate (Rp) of 32 P can be estimated as :
Rp = N Φ δ (3)
where N and δ are the number of atoms and neutron capture cross section ( 0.9×10 –24 cm 2 /atom) of 31 P, respectively, and Φ is the neutron flux (neutron / (cm 2 sec)) of the nuclear reactor. If the detection efficient (ε) of the detector for 32 P is 1.0, the decay rate (Rd) and the activity (A) of 32 P in the nuclear reactor can be approximately estimated as a function of the number (N*) of 32 P atoms as follows:
Rd = NΦ δ ( e –t ) (4)
and A = λ N* = Rp – Rd (5)
Where is the decay constant of 32 P, t is the neutron irradiation time in the nuclear reactor and the half life (t1/2) of 32 P is 14.3 days.
Write down the equations for the nuclear reactions for the production of 14 C and 3 T by the bombardment of nitrogen 14 N atoms in the atmosphere with neutrons in the cosmic ray.
Model Answer
14 1 14 1
7 0 6 1N + n C + H
14 1 12 3
7 0 6 1N + n C + T
Give the equation showing the relation between the original activity (Ao) and final activity (A) as function of time for a living animal or plant.
Model Answer
A = N, Ao = N o and N = No e –t
A / Ao = N / No = e –t
and A = Ao e –t
The activity of 14 C in an ancient wood boat is found to be 10.2 cpm/g of carbon. Calculate the age of the ancient boat.
Model Answer
N = No e –t
If N = 1/2 No, t = λ t1/2
then 1/2 No = No e –t 1/2
= 2.303 log 0.5 / t1/2 = 0.693 / t1/2
For C-14, = 0.693 / 5730 = 1.2×10 –4
Also A = Ao e –t
10.2 = 16.5 e –1.2 × 10 –4 t
and t = 4008 years
A 10 mg sample of pure H3PO4 is irradiated by neutrons with a neutron flux of 1.00×10 13 n cm –2 sec –1 for one hour in a nuclear reactor. Calculate the activity of the sample in cps (counts / second) and Ci. (Ci = Curie, 1 Ci 3.7×10 10 cps, atomic weight: H = 1, P = 31, O = 16)
Model Answer
A = Rp – Rd = N Φ δ – N Φ δ (e –t ) = N Φ δ (1– e –t )
and = 0.693 / (14.3 × 24 × 60 × 60) = 5.61×10 –7
N = [(10×10 –3 ) / 98] × 6×10 23 = 6.12×10 19
A = N Φ δ (1– e –t ) = (6.12×10 19 )(1.00×10 13 )(0.9×10 –24 )(1 – e –5.61×10–7× 60 × 60 )
and A = 1.11×10 6 cps = 1.11×10 6 / (3.7×10 10 ) Ci = 3×10 –5 Ci = 0.03 mCi
The radioisotope 32 P can be used to measure the volume of water in a pool or the blood volume of an animal. A 2.0 cm 3 solution of 1.0 Ci/ cm 3 32 P was injected into a pool. After mixing well, the activity of 1.0 cm 3 of water in the pool was found to be 12.4 cps (counts / second). Calculate the volume of water (L) in the pool. (Ci = Curie, 1 Ci 3.7×10 10 cps)
Model Answer
Total amount of 32 P is constant after and before the injection,
so, Vo Ao = Vx Ax (V = volume, A = Activity, x for pool water)
2.0 × 1.0 = Vx (12.4 / (3.7×10 10 )
and Vx(pool water) = 5.97×10 9 cm 3 = 5.97×10 6 dm 3