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 $50rad$of gamma radiation. What is that amount in grays?

Short 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-by-step solution

Given information (part a)

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

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 $70.0mkg$.

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

Explanation (part a)

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

role="math" localid="1652179518497" $70.0\cancel{\mathrm{kg}}\times \frac{4.20\mu \mathrm{Ci}}{1\cancel{\mathrm{kg}}}=294.0\mu \mathrm{Ci}$

As a result, a $70.0-kg$patient requires role="math" localid="1652179660922" $294\mu Ci$of iodine-$131$.

Given information (part b)

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

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:

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

$50rad$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 $0.5Gy$.