Question 297: Atoms & Nuclei

Question

A solution containing active cobalt $${^{60}_{27}}Co$$ having activity of $$0.8$$ $$\mu Ci$$ and decay constant $$\lambda $$ is injected in an animal's body. If $$1\,c{m^3}$$ of blood is drawn from the animal's body after $$10$$ hrs of injection, the activity found was $$300$$ decays per minute What is the volume of blood that is flowing in the body ? $$\left( {\,\,Ci = 3.7 	imes {{10}^{10}}\,} ight.$$ decays per second and at $$t=10$$ hrs $$\left. {{e^{ - \lambda t}} = 0.84} ight)$$

Accepted Answer

Initial activity, N
o
= 0.8 $$\mu $$
Ci
Activity at time t, N = N
0
e
$$-$$$$\lambda $$t
Activity in 1 cm
3
blood after 10 hr, n = 300 decays per minute
= $${{300} \over {60}}\,dps$$
= 5 dps.
Activity in whole blood after to hr = N
0
e
$$-$$$$\lambda $$$$ 	imes $$10
$$	herefore\,\,\,\,$$ Volume of the total blood = $${{{N_0}{e^{ - 10\lambda }}} \over n}$$
= $${{0.8 	imes {{10}^{ - 7}} 	imes 3.7 	imes {{10}^{10}} 	imes 0.84} \over 5}$$
= 4.97 $$ 	imes $$ 10
3
cm
3
= 4.97 litres
$$ \simeq $$ 5 liters.

Answer

$$6$$ liters

Answer

$$7$$ liters

Answer

$$4$$ liters

Answer

$$5$$ liters

Atoms & Nuclei

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