Question

the isotope has a half life of 5715 years. now there are 40g of the isotope. How much will remain after 1600 years. round to 4 decimal places

Answer 1

Category ------------ Nuclear chemistry

Sub-category --------- Radioactivity

ANSWER

The remaining amount of isotope after 1600 years is 32.9444 grams

Step-by-step explanation

Given that;

The half life of the isotope is 5715 years

The initial mass of the isotope is 40 grams

The decay time is 1600 years

Follow the steps below to find the remaining mass after 1600 years

`\text{ A\lparen t\rparen= A}_o((1)/(2))^{\frac{t}{t_{(1)/(2)}}}`

Where

A(t) is the amount of mass remaining after time t

Ao is the initial amount of mass of the substance

t1/2 is the half-life of the substance

t is the decay time

Substitute the given data into the above formula

`\begin{gathered} \text{ A\lparen t\rparen = 40 \lparen}\frac{\text{ 1}}{\text{ 2}})^{(1600)/(5715)} \\ \\ \text{ A\lparen t\rparen = 40 \lparen}\frac{\text{ 1}}{\text{ 2}})^(0.279965) \\ A(t)\text{ = 40 \lparen0.5\rparen}^(0.279965) \\ \text{ A\lparen t\rparen = 40 }*\text{ 0.8236109} \\ \text{ A\lparen t\rparen = 32.9444 grams} \end{gathered}`

Therefore, the remaining amount of isotope after 1600 years is 32.9444 grams