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Chapter 5: Q. 5.75 (page 165)

If the amount of radioactive phosphorus- $32$ , used to treat leukemia, in a sample decreases from $1.2 mg$ to $0.30 mg$ in $28.6$ days, what is the half-life of phosphorus- $32$ ? $(5.4)$

Short Answer

Expert verified

$1 h a l f - l i f e p e r i o d f o r P - 32 = \frac{28.6 days}{2 half lives} 脳 1 h a l f l i f e .$

Phosphorus- $32$ has a half-life of $14.3$ days.

Step by step solution

01

Given information

Half-life: A radioisotope's half-life is the time it takes for half of a sample to decay. In $28.6$ days, the $P - 32$ sample drops from $1.2 m g$ to $0.30 m g .$

To begin, figure out how many half-lives are needed to reduce the sample from $1.2 m g$ to $0.30 m g$ in $28.6$ days.

$1.2 mg P - 32 \overset{1 half-life}{鉄�} 0.6 mg P - 32 \overset{2 half-lives}{鉄�} 0.3 mg P - 32$

In $28.6$ days, two half-lives are required to reduce the $P - 32$ sample from $1.2 mg$ to $0.30 mg .$

02

Explanation

Calculate the half-life of $P - 32$ :

The following are the equality and conversion factors:

$2 half - lives for P - 32 = 28.6 days$

$\frac{28.6 days}{2 half - lives} o r \frac{2 half - lives}{28.6 days}$

03

Conclusion

Therefore

$1 h a l f - l i f e p e r i o d f o r P - 32$ $= \frac{28.6 days}{2 half lives} 脳 1 h a l f l i f e .$

Phosphorus- $32$ has a half-life of $14.3$ days.

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Most popular questions from this chapter

Identify each of the following:

a. ${}_{- 1}^{0}X$

b. ${}_{2}^{4}X$

c. ${}_{0}^{1}X$

d. ${}_{18}^{38}X$

e. ${}_{6}^{14}X$

Complete each of the following nuclear equations:

$? + \frac{59}{27} Co 鉄� \frac{56}{25} Mn + \frac{4}{2} He$

b. $? 鉄� {}_{7}^{14}N + {}_{- 1}^{0}e$

c. ${}_{- 1}^{0}e + {}_{36}^{76}{Kr} 鉄� ?$

d. ${}_{2}^{4}{He} + {}_{95}^{241}{Am} 鉄� ? + 2 {}_{0}^{1}n$

Indicate whether each of the following is characteristic of the fission or fusion process or both:

a. Very high temperatures are required to initiate the reaction.

b. Less radioactive waste is produced.

c. Hydrogen nuclei are the reactants.

d. Large amounts of energy are released when the nuclear reaction occurs.

If the amount of radioactive iodine- $123$ , used to treat thyroid cancer, in a sample decreases from $0.4$ my to $0.1 mg$ in $26.4 h$ , what is the half-life of iodinc- $123$ ? (5.4)

Complete each of the following nuclear equations: $(5.2)$

a. ${}_{2}^{4}{He} + {}_{7}^{14}N 鉄� ? + {}_{1}^{1}H$

b. ${}_{2}^{4}{He} + {}_{13}^{27}{Al} 鉄� {}_{14}^{30}{Si} + ?$

c. ${}_{0}^{1}n + {}_{92}^{235}U 鉄� {}_{38}^{90}{Sr} + 3 {}_{0}^{1}n + ?$

d. ${}_{12}^{23 m}{Mg} 鉄�$ $? + {}_{0}^{0}纬$

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