Complete the table for the radioactive isotope.Round your answer to two decimal places. $$\begin{array} { | c | c | c | c | }
\hline \text { Isotope } & \begin{array} { c }
\text { Half-life } \
\text { (years) }
\end{array} & \text { Initial Quantity } & \begin{array} { c }
\text { Amount after 1000 } \
\text { years }
\end{array} \
\hline { } ^ { 239 } \mathrm { Pu } & 24,100 & 2.4 g & --\
\hline
\end{array}$$
A)Amount after 1000 years: $4.33 \mathrm {~g}$
B)Amount after 1000 years: $5.33 \mathrm {~g}$
C)Amount after 1000 years: $3.33 \mathrm {~g}$
D)Amount after 1000 years: $6.33 \mathrm {~g}$
E)Amount after 1000 years: $2.33 \mathrm {~g}$

Question

Complete the table for the radioactive isotope.Round your answer to two decimal places. $$\begin{array} { | c | c | c | c | } 
\hline \text { Isotope } & \begin{array} { c } 
\text { Half-life } \
\text { (years) }
\end{array} & \text { Initial Quantity } & \begin{array} { c } 
\text { Amount after 1000 } \
\text { years }
\end{array} \
\hline { } ^ { 239 } \mathrm { Pu } & 24,100 & 2.4 g & --\
\hline
\end{array}$$
A)Amount after 1000 years: $4.33 \mathrm {~g}$
B)Amount after 1000 years: $5.33 \mathrm {~g}$
C)Amount after 1000 years: $3.33 \mathrm {~g}$
D)Amount after 1000 years: $6.33 \mathrm {~g}$
E)Amount after 1000 years: $2.33 \mathrm {~g}$

Quizplus · Accepted Answer

The amount of a radioactive isotope after a certain period can be calculated using the formula $A = P(1/2)^{t/T}$, where $A$ is the amount remaining, $P$ is the initial quantity, $t$ is the time elapsed, and $T$ is the half-life of the isotope. For $^{239}Pu$ with a half-life of 24,100 years, an initial quantity of 2.4 g, and a time period of 1000 years, the calculation is $2.4(1/2)^{1000/24100}$, which results in approximately $2.33$ g remaining after 1000 years.

Complete the Table for the Radioactive Isotope A)Amount After 1000 Years