A small volume of a solution which contained a radioactive isotope of sodium had an activity of 12000 dis/min when it was injected into the blood stream of a patient After 30hours the activity of 1cm cube of the blood was found to be 0.5 dis/min. If the half life of the sodium isotope is taken as 15hours estimate the volume of blood in the patient
@JSP Nope I don't hate them
@JSP Nope I don't hate them
Answers & Comments
Explanation:
The activity varies according to the equation,
A(t)=A
0
e
−λt
or, A(t)=A
0
(
2
1
)
t/T
1/2
In the problem, A (t=5hr)=296 disintegrations/min,
60
296
=A
0
(
2
1
)
5/15
or, A
0
=
60
296
×2
1/3
=6.22 disintegrations/sec.
= the initial activity of 1 cc. of blood.
If the total volume of blood is V cc.,
6.22 V=3.7 ×10
10
×10
−6
⇒V=5.9 ℓ.
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Verified answer
Answer:
[tex]5000cm^{3}[/tex]
Explanation:
Let [tex]V cm^{3}[/tex] be the volume of blood
Initial activity is [tex]\frac{16000}{V}[/tex] per minute per [tex]cm^{3}[/tex]
0.8 =[tex]\frac{16000}{V}[/tex] exp−0.693 × [tex]\frac{30}{15}[/tex]
=[tex]\frac{ 4 123 }{V}[/tex]
∴ V = [tex]5000cm^{3}[/tex]
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{ REMOVED }