Question

the half - life of cr - 51 is 28 days, if a sample had 510 g, how much cr was there 168 days ago?

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t\) is the time elapsed and \(T\) is the half - life.
Given \(t = 168\) days and \(T=28\) days, then \(n=\frac{168}{28}=6\).

Step2: Use the radioactive decay formula

The formula for the amount of a radioactive substance remaining is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount and \(n\) is the number of half - lives.
Given \(N_0 = 510\) g and \(n = 6\), then \(N=510\times(\frac{1}{2})^6\).
Since \((\frac{1}{2})^6=\frac{1}{64}\), then \(N = 510\times\frac{1}{64}=\frac{510}{64}=7.96875\approx7.97\) g.

Answer:

\(7.97\) g