In a sample initially, there are an equal number of atoms of two radioactive isotopes A and B. 3 days later, the number of atoms of A is twice that of…

Question

In a sample initially, there are an equal number of atoms of two radioactive isotopes A and B. 3 days later, the number of atoms of A is twice that of B. The half-life of B is 1.5 days. What is the half-life (in days) of isotope A?

MARKS Content Team · Accepted Answer

Correct answer: 3. A B t=0 N_0 N_0 t_0=3 days 2N N 2N=N_0(0.5)^(t0/τ1) N=N_0(0.5)^(t0/τ2) 2=(0.5)^(t0(1τ1−1τ2)) 0.5^(−1)=(0.5)^(3τ1−2) ⇒-1=3τ_1-2 ∴τ_1=3 days

In a sample initially, there are an equal number of atoms of two radioactive isotopes $A$ and $B$ . $3$ days later, the number of atoms of $A$ is twice that of $B$ . The half-life of $B$ is $1.5$ days. What is the half-life (in days) of isotope $A$ ?

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