Question

The radioactive isotope 133 54Xe  is used in pulmonary respiratory studies to image the blood flow and the air reaching the lungs. The half-life of this isotope is 5 days.

A hospital needs 0.100 g of 133 54Xe for a lung-imaging test. If it takes 10days to receive the shipment, what is the minimal amount mXe of xenon that the hospital should order?

Express your answer numerically in grams

Answer 1

Half-life of the isotope = T_1/2 = 5 days

Decay constant =

= 0.13863 days^-1

Minimum amount of the radioactive material the hospital orders = N₀

Amount the hospital needs for testing = N = 0.1 g

Time taken to receive the delivery = T = 10 days

N₀ = 0.4 g

Minimum amount of the radioactive material the hospital needs to orders = 0.4 g