Activities of three radioactive substances A, B and C are...

Activities of three radioactive substances $A, B$ and $C$ are represented by the curves $A, B$ and $C,$ in the figure. Then their half-lives $T\dfrac{1}{2}$ \left(A\right): T\dfrac{1}{2} $\left(B\right): T\dfrac{1}{2}\left(C\right)$ are in the ratio:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then

Options

A $2: 1: 1$
B $3: 2: 1$
C $2: 1: 3$
D $4: 3: 1$

Correct answer

C. $2: 1: 3$

Step-by-step solution

R = {R}_{0}{e}^{- \lambdat} $</p><p>$ lnR = - \lambda \cdot nt + ln{R}_{0} $</p><p>Slope = \dfrac{\ln 2}{{t}_{1/2}} = \lambda$

${T}_{1}\left(A\right): {T}_{1}\left(B\right): {T}_{1}\left(C\right) = 2: 1: 3$

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