Two radioactive materials X1 and X2 have decay constants 11λ and λ respectively. If initially they have the same number of nuclei , then ratio of number of nuclei of X1 to X2 will be 1e2 after a time-
A
19λ
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B
110λ
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C
111λ
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D
15λ
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Solution
The correct option is D15λ At some instant time t, number of undecayed atoms exists is,
N1=N0e−11λt and N2=N0e−λt
It is given that,
N1N2=1e2
⇒1e2=N0e−11λtN0e−λt
⇒1e2=e−11λte−λt
⇒e−2=e−(11−1)λt
Taking log on both sides, we get,
⇒10λt=2
⇒t=210λ=15λ
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Hence, (D) is the correct answer.