Question

For the given graph between decay rate and time find half-life (where R = decay rate)

• A. a. 10 / 3 ln⁡2
• B. b. 20 / 3 ln⁡2
• C. c. 3 / 20 ln⁡2
• D. d. 3 / 10 ln⁡2

Answer 1

The correct option is B

b. 20 / 3 ln⁡2

$$\begin{gathered} \mathrm{Answer}(\mathrm{B})\mathrm{is}\mathrm{correct} \\ \mathrm{R}={\mathrm{R}}_{\circ }{\mathrm{e}}^{-\mathrm{\lambda t}} \\ \mathrm{In}\mathrm{R}=\mathrm{In}{\mathrm{R}}_{\circ }-\mathrm{\lambda t} \\ \mathrm{Slope}=-\mathrm{\lambda }=-6/40 \\ \mathrm{\lambda }=3/20 \\ {\mathrm{t}}_{1/2}=\mathrm{In}2/\mathrm{\lambda }=\mathrm{In}2/3\times 20=20/3\mathrm{In}2 \end{gathered}$$