The half-life of a radioactive element which has only 1/32 of its original mass left after elapsed of 60 days is:
Correct answer: D. 12 days
- A. 30 days
- B. 20 days
- C. 15 days
- D. 12 days
Explanation
As: N=N0 ×(1/2)t/TGiven that N/N0 =1/32 and t=60 days, we can substitute these values into the equation: 1/32=(1/2)60/TTaking the natural logarithm of both sides gives: ln(1/32)=60/T ln(1/2)Solving for T gives: T=60 ln(1/2) /ln(1/32) =60(-0.693)/(-3.465) =60(0.2) =12So, the half-life of the radioactive element is 12 days.
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About Half-life and Rate of Decay
Half-life is the time required for half the unstable nuclei in a sample to decay, and it remains constant for a particular radioactive nuclide. Questions use the exponential decay law, decay constant, activity, remaining quantity and mean life. Radioactive decay is random for individual nuclei but predictable for large samples.
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