Q23 of 94 Page 442

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes.

(a) What is the decay constant of the sample?


(b) What is its half-life?


Initial Activity = 500

Final activity = 200


a) We know that,




Where,


A= Activity of the substance


A0 = Initial activity


t = time=50 mins


λ = decay constant


so,







b) Half life




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21

Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 μ Ci at t = 0.

(a) What is its activity at t = 4.0 days?


(b) What is its decay constant at t = 4.0 days?


 22

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?


 24

The count rate from a radioactive sample falls from 4.0 × 106 per second to 1.0 × 106 per second in 20 hours. What will be the count rate 100 hours after the beginning?

 25

The half-life of 226Ra is 1602 y. Calculate the activity of 0.1g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226 g mol–1 and that of Cl to be 35.5 g mol–1.