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A small quantity of solution containing {Na}^{24} radio nuclid

Question

Hard

Solving time: 4 mins

A small quantity of solution containing $Na^{24}$ radio nuclide ( half- life $= 15$ h) of activity $1.0$ microcurie is injected into the blood of a person. A sample of the blood of volume $1 cm^{3}$ taken after 5 h shows an activity of 296 disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person. $(1$ curie $= 3.7 \times 1 0^{10}$ disintegrations per second $)$

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Book:

Optics And Modern Physics (DC Pandey)

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Scarlett Discussed

A small quantity of solution containing

Na^{24}

radio nuclide ( half- life

= 15

h) of activity

1.0

microcurie is injected into the blood of a person. A sample of the blood of volume

1 cm^{3}

taken after 5 h shows an activity of 296 disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person.

(1

curie

= 3.7 \times 1 0^{10}

disintegrations per second

)

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

∵ λ =

Disintegration constant

\frac{0.693}{t _{1/2}} = \frac{0.693}{15} h^{- 1} = 0.0462 h^{- 1}

Let

R_{0} =

initial activity

= 1

microcurie

= 3.7 \times 1 0^{4}

disintegrations per second

r =

Activity in

1 cm^{3}

of blood at

t = 5 h

= \frac{296}{60}

disintegration per second

= 4.93

disintegration per second, and

R =

Activity of whole blood at time

t = 5 h

Total volume of blood should be

V = \frac{R}{r} = \frac{R _{0} e ^{- λ t}}{r}

Substituting the values, we have

V = (\frac{3.7 \times 1 0 ^{4}}{4.93}) e^{- (0.0462) (5)} cm^{3}

V = 5.95 \times 1 0^{3} cm^{3} or V = 5.95 L

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Question Text	A small quantity of solution containing $Na^{24}$ radio nuclide ( half- life $= 15$ h) of activity $1.0$ microcurie is injected into the blood of a person. A sample of the blood of volume $1 cm^{3}$ taken after 5 h shows an activity of 296 disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person. $(1$ curie $= 3.7 \times 1 0^{10}$ disintegrations per second $)$
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	120

Text solutionVerified

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