Question

how much of a radioactive kind of zinc will be left after 2 hours if the half - life is 1 hour and you start with 259,288 grams? grams

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t = 2\) hours (time elapsed) and \(T = 1\) hour (half - life). So \(n=\frac{2}{1}=2\).

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0=259288\) grams (initial amount) and \(n = 2\).
Substitute the values: \(N=259288\times(\frac{1}{2})^2\).
First, calculate \((\frac{1}{2})^2=\frac{1}{4}\).
Then \(N = 259288\times\frac{1}{4}\).
\(N=\frac{259288}{4}=64822\).

Answer:

\(64822\)