Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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# The Decay Constant of 238u is 4.9 × 10−18 S−1. (A) What is the Average-life of 238u? (B) What is the Half-life of 238u? (C) by What Factor Does the Activity of a 238u Sample Decrease in 9 × 109 Years? - Physics

#### Question

The decay constant of 238U is 4.9 × 10−18 S−1. (a) What is the average-life of 238U? (b) What is the half-life of 238U? (c) By what factor does the activity of a 238U sample decrease in 9 × 109 years?

#### Solution

Given:
Decay constant, lambda = 4.9 xx 10^-18  "s"^-1

(a) Average life of uranium (tau) is given by

tau = 1/lambda

= 1/(4.9 xx 10^-18)

= 1/4.9 xx 10^18  "s"

= 10^16/(4.9 xx 365 xx 24 xx 36)  "years"

= 10^16/(4.9 xx 365 xx 24 xx 36)  "years"

= 6.47 xx 10^-7 xx 10^16 "years"

= 6.47 xx 10^9  "years"

(b) Half-life of uranium (T_"1/2") is given by

T_"1/2" = 0.693/lambda = 0.693/(4.9 xx 10^-18)

= 0.693/4.9 xx 10^18  "s"

= 0.1414 xx 10^18  "s"

= (0.1414 xx 10^18)/(365 xx 24 xx 3600)

= (1414 xx 10^12)/(365 xx 24 xx 36)

= 4.48 xx 10^-3 xx 10^12

= 4.5 xx 10^9 years

(c) Time, t = 9 × 109 years
Activity (A) of the sample, at any time t, is given by

A = A_0/2^(t/T_"1/2")

Here ,  A_0  = Activity of the sample at t = 0

therefore A_0/A = 2^((9 xx 10^9)/(4.5 xx 10^9)) = 2^2 = 4

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Solution The Decay Constant of 238u is 4.9 × 10−18 S−1. (A) What is the Average-life of 238u? (B) What is the Half-life of 238u? (C) by What Factor Does the Activity of a 238u Sample Decrease in 9 × 109 Years? Concept: Radioactivity - Law of Radioactive Decay.
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