Question

A sample of the radioactive substance is found 90% of its initial amount after on day. What % of the original sample can be found after 3 days?

• A. 81
• B. 72.9
• C. 25
• D. 65.61

Answer 1

Answer: (B)

72.9

$A_t=A_o{e}^{-\lambda t}\Rightarrow A_t=A_o{e}^{-3\lambda }$

$0\cdot 9=e^{-\lambda }{A}_t=a_o{e}^{ln\left(\frac{9}{10}\right)\times 3}$

$ln\left(\frac{9}{10}\right)=-\lambda =A_o(\frac{9}{10}{)}^3$

$\lambda =ln\left(\frac{10}{9}\right)=72\cdot 9A_o$

i.e. $72\cdot 9$% after 3 days.