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 Ct=Tlog1.3log2 AT→B λ=ln2T NA=N0e−λt NB=N0(1−e−λt) NBNA=0.3 N0(1−e−λt)N0e−λt=0.3 1−e−λt=0.3e−λt 1=1.3e−λt 11.3=e−λt ln11.3=−λt=−ln2Tt t=Tlog1.3log2