Q. 5.27 - An Introduction to General, Organic, and Biological Chemistry

Question

a) The recommended dosage of iodine-$131$ is $4.20\mu \mathrm{Ci}/\mathrm{kg}$ of body mass, How many microcuries of iodine-$131$ are needed for a $70.0$-kg person with hyperthyroidism?

b) A person receives $50 rad$ of gamma radiation. What is that amount in grays?

Step-by-Step Solution

Answer

(part a) $294 \mu \mathrm{Ci}$ of iodine-$131$ are required for a$70.0-\mathrm{kg}$ patient.

(part b) Gamma radiation received by person is $0.5 \mathrm{Gy}$.

Step 1: Given information (part a)

A $70.0-kg$ patient requires $294 \mu \mathrm{Ci}$ of iodine-$131$.

Step 2: Explanation (part a)

(part a) The number of nuclear disintegrations per second is used to evaluate the sample's activity. The unit of activity measurement is the curie $\left(Ci\right)$.

Iodine-$131$ dosage is $4.20\mu mCi/kg$ of body mass.

Calculate how many microcuries of iodine-$131$ are required for a patient weighing $70.0 mkg$.

$4.20\mu \mathrm{Ci}=1 \mathrm{kg}$

Step 3: Explanation (part a)

Calculate the iodine-$131$ needed using the conversion factor.

$70.0 \cancel{\mathrm{kg}}\times \frac{4.20\mu \mathrm{Ci}}{1 \cancel{\mathrm{kg}}}=294.0\mu \mathrm{Ci}$

As a result, a $70.0-kg$ patient requires $294\mu Ci$ of iodine-$131$.

Step 4: Given information (part b)

The amount of gamma radiation a person receives is $0.5 Gy$.

Step 5: Explanation (part b)

(part b) A rad is a measurement unit for the quantity of radiation absorbed by a gram of material, such as human flesh. The $SI$ unit for absorbed dose measurement is the grey $\left(Gy\right)$.

The rad is a typical measurement unit for the amount of radiation absorbed by a medium.

The following is the relationship between rad and grey:

$1Gy=100\mathrm{rad}.$

$50 rad$ of gamma radiation is given to the person.

Calculate the received gamma radiation in grey using the conversion factor.

$50 \cancel{\mathrm{rad}}\times \frac{1 \mathrm{Gy}}{100 \cancel{\mathrm{rad}}}=0.5 \mathrm{Gy}$

As a result, the gamma radiation a person receives is $0.5 Gy$.