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Q.

For a certain radioactive substance, it is observed that after 4 hours, only 6.25% of the original sample is left un-decayed. Choose the only wrong statement from the following:

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a

the decay constant of the sample is ln(2) hr-1

b

after a further 4 hours, the amount of the substance left over would be only 0.39% of the original amount. 

c

the half life of the sample is 1 hr.

d

the mean life of the sample is 12 hr.

answer is B.

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Detailed Solution

6.25%=6.25100=116=124

Hence 4 hours are equal to 4 half lives. Therefore, the half life of the substance is 1 hour.

 The decay constant = ln2half lifeln2 per hr, 

Mean life = 1decay constant

                = 1ln2 hour = 10.693hr

After further four hours (8 hours from starting), the amount of substance left would be:
NN0 = 128 = 0.0039
Percentage of amount of substance left would be NN0 ×100 % =  0.0039 ×100 % = 0.39 %.

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