Question

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

Answer 1

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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Answer 2

Answer:

$5000cm^{3}$

Explanation:

Let $V cm^{3}$ be the volume of blood

Initial activity is $\frac{16000}{V}$ per minute per $cm^{3}$

0.8  =$\frac{16000}{V}$ exp−0.693 × $\frac{30}{15}$

       =$\frac{ 4 123 }{V}$

∴ V = $5000cm^{3}$

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