Question

Gold-198 is a radioactive isotope that is used to treat several types of cancer. Its first order decay has a half-life of 2.7 days.

a) What is the rate constant of the reaction?
b) How many grams must a physician order for a treatment that will begin in 11 days, if approximately 15 g of Gold-198 is needed for treatment?

Answer 1

The rate constant of the reaction is approximately 0.257. The physician must order approximately 5.122 grams of Gold-198 for the treatment.

Step-by-step explanation:

a) The rate constant (k) can be calculated using the formula for first-order decay:

k = ln(2) / half-life

Substituting the values given, we get:

k = ln(2) / 2.7

k ≈ 0.257

Therefore, the rate constant is approximately 0.257.

b) To calculate the grams of Gold-198 needed for a treatment starting in 11 days, we can use the formula for exponential decay:

grams = initial grams * e^(-k * time)

Substituting the values given, we get:

grams = 15 * e^(-0.257 * 11)

grams ≈ 5.122

Therefore, the physician must order approximately 5.122 grams of Gold-198 for the treatment.