Question

tungsten, w-181, is a radioactive isotope with a half life of 121 days. if a medical lab purchases 24 kg of w-181, how much will be left after 1 year? a 24 kg b 12 kg c 6 kg d 3 kg

Explanation:

Step1: Calculate number of half - lives in a year

A year has approximately 365 days. The half - life of W - 181 is 121 days. The number of half - lives \(n=\frac{365}{121}\approx3\) (since \(\frac{365}{121}\approx3.02\), we can approximate \(n = 3\) for simplicity).

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount, \(n\) is the number of half - lives, and \(N\) is the remaining amount. Here, \(N_0 = 24\space kg\) and \(n = 3\).
So \(N=24\times(\frac{1}{2})^3=24\times\frac{1}{8} = 3\space kg\).

Answer:

D. 3 kg