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Question

# 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 D 15λAt 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 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.

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