Question

a scientist is studying a radioactive element that has a half - life of 63 years. choose the correct answers from the drop - down menus to complete each statement about the element.
it will take years for half of the sample to decay.
in 189 years, of the sample will be left.
scientists can figure out how old a sample is by multiplying the by the length of the half - life.

Explanation:

Step1: Recall the definition of half - life

The half - life is the time it takes for half of a radioactive sample to decay. Given the half - life is 63 years, so it will take 63 years for half of the sample to decay.

Step2: Calculate the number of half - lives in 189 years

The number of half - lives \(n=\frac{189}{63}=3\).
The amount of the sample left \(N = N_0\times(\frac{1}{2})^n\). Substituting \(n = 3\), we get \(N=N_0\times\frac{1}{8}\) (where \(N_0\) is the initial amount of the sample).

Step3: Recall the formula for radioactive dating

The formula for radioactive dating is \(t=n\times T\) (where \(t\) is the age of the sample, \(n\) is the number of half - lives, and \(T\) is the half - life). So scientists can figure out how old a sample is by multiplying the number of half - lives by the length of the half - life.

Answer:

1. 63
2. \(\frac{1}{8}\)
3. number of half - lives