Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Radioactive 131i Has a Half-life of 8.0 Days. a Sample Containing 131i Has Activity 20 µCi at T = 0. (A) What is Its Activity at T = 4 Days? (B) What is Its Decay Constant at T = 4.0 Days? - Physics

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Question

Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?

Solution

Given:
Half-life of radioactive 131I, T1/2 = 8 days
Activity of the sample at t = 0, A0 = 20 µCi
Time, t = 4 days

(a) Disintegration constant, `lambda = 0.693/T_"1/2" = 0.0866`

Activity (A) at t = 4 days is given by

`A = A_0e^-"λt"`

⇒ `A = 20 xx 10^-6 xx e^(-0.0866 xx 4)`

= `1.41 xx 10^-6 "Ci" = 14  "µCi"`

(b) Decay constant is a constant for a radioactive sample and depends only on its half-life.

`lambda = 0.693/[[8 xx 24 xx 3600]]`

= `1.0026 xx 10^-6  "s"^-1`

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Solution Radioactive 131i Has a Half-life of 8.0 Days. a Sample Containing 131i Has Activity 20 µCi at T = 0. (A) What is Its Activity at T = 4 Days? (B) What is Its Decay Constant at T = 4.0 Days? Concept: Radioactivity - Introduction of Radioactivity.
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