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 submit

Explanation:

Step1: Understand half - life concept

The half - life formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^{\frac{t}{T_{1/2}}}\), where \(N\) is the final amount, \(N_0\) is the initial amount, \(t\) is the time elapsed, and \(T_{1/2}\) is the half - life. Here, \(N_0 = 259288\) grams, \(t = 2\) hours, and \(T_{1/2}=1\) hour.

Step2: Calculate the number of half - lives

The number of half - lives \(n=\frac{t}{T_{1/2}}=\frac{2}{1} = 2\).

Step3: Apply the half - life formula

Substitute the values into the formula: \(N=259288\times(\frac{1}{2})^{2}\). First, calculate \((\frac{1}{2})^{2}=\frac{1}{4}\). Then, \(N = 259288\times\frac{1}{4}\).

Step4: Perform the multiplication

\(259288\div4 = 64822\).

Answer:

64822