Question

if a 100g sample of a radioactive element decays to 25g in 4 days what is the half life of the element?

Answer 1

ANSWER

The half-life of the sample is 50 days

EXPLANATION

Given thanks

The initial mass of the sample is 100g

The remaining mass of the sample is 25g

Time = 4 days

To find the half-life of the mass, follow the steps below

Step 1: Write the half life formula

$\text{ N }=\text{ N}_O(\frac{1}{2})^{\frac{t}{\iota}}$

Where

$\begin{gathered} \text{ N is the undecayed sample} \\ \text{ N}_O\text{ is the decayed sample} \\ \iota\text{ is the half-life} \end{gathered}$

Step 2: Substitute the given data to find the half-life of the sample

$\begin{gathered} 25\text{ }=\text{ 100\lparen}\frac{1}{2})^{\frac{t}{\iota}} \\ Divide\text{ both sides by 100} \\ \frac{25}{100}=\text{ }\frac{100}{100}(\frac{1}{2})^{\frac{t}{\iota}} \\ \\ \frac{1}{4}\text{ }=\text{ \lparen}\frac{1}{2})^{\frac{t}{\iota}} \\ \\ (\frac{1}{2})^2\text{ }=\text{ \lparen}\frac{1}{2})^{\frac{t}{\iota}} \\ 2\text{ }=\frac{t}{\iota} \\ \text{ Recall, that t }=\text{ 100 days} \\ \text{ 2 }=\text{ }\frac{100}{\iota} \\ \text{ cross multiply} \\ \text{ 2}\iota\text{ }=\text{ 100} \\ \text{ Divide both sides by 2} \\ \iota\text{ }=\text{ }\frac{100}{2} \\ \text{ }\iota\text{ }=\text{ 50 days} \end{gathered}$

Hence, the half-life of the sample is 50 days