Q. 5.28 - An Introduction to General, Organic, and Biological Chemistry

Question

a) The dosage of technetium-$99m$ for a lung scan is $20$. $\mu \mathrm{CM}/\mathrm{kg}$ of body mass. How many millicuries of technetium-99m should be given to a$50.0$-kg person $(1\mathrm{mCi}=1000\mu \mathrm{Ci})?$

b) Suppose a person absorbed $50 mrad$ of alpha radiation. What would be the equivalent dose in millisieverts ?

Step-by-Step Solution

Answer

(part a) $1\mathrm{mCi}$ technetium required for a $50.0-\mathrm{kg}$ patient.

(part b) The person absorbed $50 mrad$ of alpha radiation, which is equivalent to $1000$ millirems.

Step 1: Given Information (part a)

For a $50.0-kg$ patient, 1mci technetium is needed.

Step 2: Explanation (part a)

(part a) The sample's activity is expressed as the number of nuclear disintegrations per second. The curie $\left(Ci\right)$ is a standard unit for measuring activity.

For a lung scan, a dose of $20\mu Ci/kg$ of body mass is advised.

Calculate how many millicuries of technetium-$99m$ are required for a patient weighing $50.0-kg$.

$20\mu \mathrm{Ci}=1 \mathrm{kg}$

Step 3: Explanation (part a)

Using conversion factors calculate the required amount of technetium- $99 \mathrm{m}$.

$50.0 \cancel{\mathrm{kg}}\times \frac{20\mu \mathrm{Ci}}{1 \cancel{\mathrm{kg}}}=1,000\mu \mathrm{Ci}$

$1,000\mu Ci$ is converted to millicuries.

$1 millicurie =1,000 \mu Ci$

Therefore,

$1,000 \mu Ci\times \frac{1 millicurie}{1,000 \mu Ci}=1millicurie$

As a result, a $50.0-kg$ patient requires $1mCi$ technetium.

Step 4: Given information (part b)

The subject was exposed to $50$ millirems of alpha radiation, or $50 mrad$.

Step 5: Explanation (part b)

(part b) The rad is a unit of measurement for the quantity of radiation absorbed by a gram of material such as body tissue.

A person is exposed to $50$ millirems of alpha radiation.

Calculate the equivalent dose in millirems using the formula below.

$Bio\log ical damage \left(rems\right) = absorbed dose \left(rads\right) \times factor$

The factor for alpha particles is $20$.

Therefore,

$Bio\log ical damage \left(mrems\right)=50\times 20 = 1,000$

As a result, the person absorbed $50$ millirems of alpha radiation.