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Q.

A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10 gm of A and 1gm of  B  is taken. The time (approximate) after which they will have same quantity remaining is

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a

6.62 years

b

5 years

c

3.2 years

d

7 years

answer is A.

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Detailed Solution

N=N012t/T1/2 ⇒NA=1012t/1 and NB=112t/2Given NA=NB⇒1012t=12t/2 ⇒10=12-t/2⇒10=2t/2.Taking log both the sides.log10=t2log102⇒1=t2 x 0.3010 ⇒t=6.62 years.
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