The recommended dosage of iodine-131 is 21 Ci/5 kg of body mass. How many microcuries of iodine-131 are needed for a 75.0-kg person with hyperthyroidism?
To find the number of microcuries required, we need to convert 21 Ci to microcuries and multiply it by the person's body mass.
1 Ci = 1,000,000 microcuries.
So, 21 Ci = 21 * 1,000,000 = 21,000,000 microcuries.
Now, we can calculate the number of microcuries needed for a 75.0-kg person:
Number of microcuries = (21,000,000 microcuries / 5 kg) * 75.0 kg
Number of microcuries = 4,200,000 microcuries/kg * 75.0 kg
Number of microcuries = 315,000,000 microcuries
Therefore, a 75.0-kg person would require 315,000,000 microcuries of iodine-131.
To calculate the required microcuries of iodine-131 for a 75.0-kg person with hyperthyroidism, we can follow these steps:
Step 1: Convert the body mass from kilograms to pounds.
1 kg = 2.20462 lbs
75.0 kg = 75.0 * 2.20462 = 165.3475 lbs
Step 2: Calculate the recommended dosage in microcuries per pound.
Since the recommended dosage is given per 5 kg of body mass, we need to calculate the dosage per pound.
21 Ci / 5 kg = (21 / 5) Ci per kg = 4.2 Ci per kg
4.2 Ci/kg * 2.20462 lbs/kg = 9.2593544 Ci/lb
Step 3: Calculate the required dosage for the person's body mass.
9.2593544 Ci/lb * 165.3475 lbs = 1530.9616 Ci
Step 4: Convert the dosage to microcuries.
1 Ci = 1,000,000 microcuries
1530.9616 Ci * 1,000,000 microcuries/Ci = 1,530,961.6 microcuries
Therefore, a 75.0-kg person with hyperthyroidism would require approximately 1,530,961.6 microcuries of iodine-131.