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The number of half lives elapsed before ...

The number of half lives elapsed before 93.75% of a radioactive sample has decayed is

A

6

B

4

C

2

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Number of half lives be obtained by using
`N=N_(0)(1/2)^(n)`
Here, `N=(100-93.75)xxN_(0)/100=6.25/100xxN_(0)`
`therefore" "(1/2)^(n)=625/10000=(5/10)^(4)=(1/2)^(4)`
or n = 4.
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Radioactive decay is a statisticle process i.e., we cannot precisely predict the timing of a particular radioactivity of a particular nucleus . The nucleus can disintegrate immediately or it may take infinite time . Simply the probability of the number of nuclei being disintegrated at any instant can be predicted . the rate at which a particular decay process in a radioactive sample is directly proportional to the number of radioactive nuclei present and thus obeys first order kinetics . the factor dN/N expresses the fraction of nuclei decayed in time dt. t_(1//2) is the time in which half of the atoms are decayed and average life is the time for the nucleus to survive before decay . 75 atoms of a radioactive species are decayed in 2 half lives (t_(1//2) = 1 hr ) if 100 atoms are taken initially . Number of atoms decayed if 200 atoms are taken in 2 hr are :

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