Question

If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.

Answer 1

Answer: $26.4\ \text{days}$

Step-by-step explanation:

Given

Half life of radioactive substance is $T_{\frac{1}{2}}=20\ \text{days}$

Initial amount $A_o=2\ \text{days}$

Amount left at any time is given by

$\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}$

It takes 26.4 days to reach 2 gm.