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 iron-59 is 45 days and its biological half-life is 600 days. Find the effective half-life of iron-59.

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 iron-59 is 45 days and its biological half-life is 600 days. Find the effective half-life of iron-59.

Quizplus · Accepted Answer

Using the formula, we have
$$\frac{1}{H_e}=\frac{1}{H_p}+\frac{1}{H_b}=\frac{1}{45}+\frac{1}{600}$$
$$\frac{1}{H_e}=\frac{8}{360}+\frac{3}{360}=\frac{11}{360}$$
$$\Rightarrow H_e=\frac{360}{11}=32\frac{8}{11}\approx \boxed{41.9 \text{ days}}$$

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

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