Question

how much of a radioactive kind of promethium will be left after 265 hours if the half - life is 53 hours and you start with 15,488 grams? grams submit

Explanation:

Step1: Find the number of half - lives

The formula to find the number of half - lives \(n\) is \(n=\frac{t}{T}\), where \(t\) is the total time and \(T\) is the half - life.
Given \(t = 265\) hours and \(T=53\) hours.
So \(n=\frac{265}{53}=5\).

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.
We know that \(N_0 = 15488\) grams and \(n = 5\).
Substitute these values into the formula: \(N=15488\times(\frac{1}{2})^5\).
First, calculate \((\frac{1}{2})^5=\frac{1}{32}\).
Then \(N = 15488\times\frac{1}{32}\).
\(15488\div32 = 484\).

Answer:

484