Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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The Half-life of 199au is 2.7 Days. (A) Find the Activity of a Sample Containing 1.00 µG of 198au. (B) What Will Be the Activity After 7 Days? Take the Atomic Weight of 198au to Be 198 G Mol−1. - Physics

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Question

The half-life of 199Au is 2.7 days. (a) Find the activity of a sample containing 1.00 µg of 198Au. (b) What will be the activity after 7 days? Take the atomic weight of 198Au to be 198 g mol−1.

Solution

Given:-

Half-life of 199Au, T1/2= 2.7 days

Disintegration constant, `lambda = 0.693/T_(1"/"2) = 0.639/(2.7 xx 24 xx 60 xx 60) = 2.97 xx 10^-6  "s"^-1`

Number of atoms left undecayed, N = `(1 xx 10^-6 xx 6.023 xx 10^23)/198`

Now, activity, `A_0 = lambdaN`

`= (1 xx 10^-6 xx 6.023 xx 10^23)/198 xx 2.97 xx 10^-6`

= 0.244 Ci


(b) After 7 days Activity,

`A = A_0e^-"λt"`

Here, `A_0 = 0.244` Ci

`therefore A = 0.244 xx e^(-2.97 xx 10^-6 xx 7 xx 3600 xx 24)`

`= 0.244 xx e^(17962.56 xx 10^-4)`

= 0.040 Ci

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Solution The Half-life of 199au is 2.7 Days. (A) Find the Activity of a Sample Containing 1.00 µG of 198au. (B) What Will Be the Activity After 7 Days? Take the Atomic Weight of 198au to Be 198 G Mol−1. Concept: Radioactivity - Introduction of Radioactivity.
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