Question

how long will it for a take for a 40 gram. the half - life of cobalt - 60 is 5.26 years sample of cobalt - 60 to decay to 5 grams? 15.78 years 17.75 days 15.15 years 17.17 years

Explanation:

Step1: Determine the number of half - lives

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N\) is the final amount, \(N_0\) is the initial amount, and \(n\) is the number of half - lives.
Given \(N_0 = 40\) grams, \(N = 5\) grams.
Substitute into the formula: \(5=40\times(\frac{1}{2})^n\).
Then \(\frac{5}{40}=(\frac{1}{2})^n\), \(\frac{1}{8}=(\frac{1}{2})^n\).
Since \(\frac{1}{8}=(\frac{1}{2})^3\), so \(n = 3\).

Step2: Calculate the time

The half - life \(T = 5.26\) years.
The time \(t=n\times T\).
Substitute \(n = 3\) and \(T = 5.26\) into the formula: \(t=3\times5.26 = 15.78\) years.

Answer:

15.78 years