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Question

A radioactive nucleus A with a half-life T, decays into a nucleus B. At t=0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by:

A
t=Tlog(1.3)
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B
t=Tlog(1.3)
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C
t=Tlog1.3log2
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D
t=Tlog(1.3)
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Solution

The correct option is C t=Tlog1.3log2
ATB
λ=ln2T
NA=N0eλt
NB=N0(1eλt)
NBNA=0.3
N0(1eλt)N0eλt=0.3
1eλt=0.3eλt
1=1.3eλt
11.3=eλt
ln11.3=λt=ln2Tt
t=Tlog1.3log2

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