Q24 of 94 Page 442

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?

We know that,



Where,


A= Activity of the substance=1 × 106 s-1


A0 = Initial activity=4 × 106 s-1


t = time=20h


λ = decay constant


So according to the problem,




Now we have to evaluate activity after 100 hours





A = 3.9× 103 disintegrations per second


Hence, the activity after 100 hours is 3.9× 103 disintegrations per second.


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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?


 23

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?


 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.

 26

The half-life of a radioisotope is 10 h. Find the total number of disintegrations in the tenth hour measured from a time when the activity was 1 Ci.