Use the following information to answer the Questions
A radioactive element used in medicine has a physical half-life $H_{p}$
(the time in which half of any quantity of the element decays) and a biological half-life $H _ { b }$ (the time in which half of an amount of this element in the body is excreted). The effective half-life $H _ { e }$ is calculated from $\frac { 1 } { H _ { e } } = \frac { 1 } { H _ { p } } + \frac { 1 } { H _ { b } } .$
-The physical half-life of sulfur-35 is 87.4 days and its biological half-life is 90 days. Find the effective half-life of sulfur-35.

Question

Use the following information to answer the Questions
A radioactive element used in medicine has a physical half-life $H_{p}$
 (the time in which half of any quantity of the element decays) and a biological half-life $H _ { b }$ (the time in which half of an amount of this element in the body is excreted). The effective half-life $H _ { e }$ is calculated from $\frac { 1 } { H _ { e } } = \frac { 1 } { H _ { p } } + \frac { 1 } { H _ { b } } .$
-The physical half-life of sulfur-35 is 87.4 days and its biological half-life is 90 days. Find the effective half-life of sulfur-35.

Quizplus · Accepted Answer

Using the formula for effective half-life, we have:

\begin{align*}
\frac{1}{H_e}&=\frac{1}{H_p}+\frac{1}{H_b}\
\frac{1}{H_e}&=\frac{1}{87.4	ext{ days}}+\frac{1}{90	ext{ days}}\
\frac{1}{H_e}&\approx0.02285	ext{ days}^{-1}\
H_e&\approx43.8	ext{ days}\
\end{align*}

Rounding to one decimal place, we get the effective half-life of sulfur-35 to be 44.3 days. Therefore, the answer is A).

Use the Following Information to Answer the Questions a Radioactive HpH_{p}Hp​

Use the Following Information to Answer the Questions
a Radioactive $H_{p}$