Chapter 11: Q50E (page 520)

Given initially 100 g of Plutonium-239, how muchtime must pass for amount to drop to $1 g$ ?

Short Answer

Expert verified

The time taken is $160.18 thousand years$ .

Step by step solution

Given data

N₀= $100 g$

N= $1 g$

Concept of Number of Nuclei which remain

The number of nuclei which remain after time $t$ is given by:

$N = N_{0} e^{- λt}$ .

Where $λ = Decay constant = \frac{\ln 2}{T_{1 / 2}}$ , $N_{0}$ is the original number of nuclei, $T_{1 / 2} =$ half-life and $N =$ is the number of nuclei at time t.

Calculate the time required from the Concept of the Number of Nuclei which remain

Plutonium 239's half-life is $24.11$ thousand years.

For nuclear decay, obtain:

$\begin{matrix} N = N_{0} e^{- λt} \\ = N_{0} e^{- (\frac{\ln 2}{T_{1 / 2}}) t} \end{matrix}$

Apply logarithm on both sides:

$\ln \frac{N}{N_{0}} = - \frac{\ln 2 \times t}{T_{1 / 2}}$

Rearrange the above equation for $t$ , substitute the values as:

$\begin{matrix} t = - \frac{T_{1 / 2}}{\ln 2} \ln (\frac{N}{N_{0}}) \\ = - (\frac{24 .11 thousand years}{\ln 2}) \ln (\frac{1 g}{100 g}) \\ = 160 .18 thousand years \end{matrix}$

Thus, the time taken is $160.18 thousand years$ .

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Given initially 100 g of Plutonium-239, how muchtime must pass for amount to drop to $1 g$ ?

Short Answer

Step by step solution

Given data

Concept of Number of Nuclei which remain

Calculate the time required from the Concept of the Number of Nuclei which remain

One App. One Place for Learning.

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Given initially 100 g of Plutonium-239, how muchtime must pass for amount to drop to1 g ?

Short Answer

Step by step solution

Given data

Concept of Number of Nuclei which remain

Calculate the time required from the Concept of the Number of Nuclei which remain

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Further Mechanics and Thermal Physics

Nuclear Physics

Energy Physics

Thermodynamics

Oscillations

Study anywhere. Anytime. Across all devices.

Given initially 100 g of Plutonium-239, how muchtime must pass for amount to drop to $1 g$ ?