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3 years ago

14

The element plutonium-239 is highly radioactive. Nuclear reactors

1 answer:

Dominik [7]3 years ago

7 0

Answer:

$2.84\cdot 10^{-5} y^{-1}$

Step-by-step explanation:

The decay rate of a radioactive isotope (also called activity of the isotope) is given by:

$r=k N$

where

r is the decay rate

k is the decay constant

N is the number of nuclei in the radioactive sample

The decay constant of a radioactive isotope is also related to the half-life of the isotope by the formula

$k=\frac{ln2}{t_{1/2}}$

where

$t_{1/2}$ is the half-life of the isotope, which is the time taken for the sample to halve, compared to its initial amount

In this problem, the half-life of plutioniun-239 is

$t_{1/2}=24,360 y$

Therefore, the k-factor (decay constant) is:

$k=\frac{ln 2}{24,360}=2.84\cdot 10^{-5} y^{-1}$

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Complete Question:

The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of D is five-halves the measure of Y. Find the measure of each angle of the deck.

Answer:

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Step-by-step explanation:

Given

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Dimension: $\angle D = \frac{5}{2}\angle Y$

Required

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$\angle D = \angle R = \frac{5}{2}\angle Y$

and

$\angle G = \angle Y$

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Substitute values for $\angle D, \angle G \ \& \angle R$

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$\frac{2}{14} * \frac{14\angle Y}{2}= 360^{\circ} * \frac{2}{14}$

$\angle Y= 360^{\circ} * \frac{2}{14}$

$\angle Y= \frac{ 360^{\circ} *2}{14}$

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$\angle Y= 51.43 ^{\circ}$

So:

$\angle G = \angle Y = 51.43 ^{\circ}$

$\angle D = \frac{5}{2}\angle Y$

$\angle D = \frac{5}{2} * 51.43^{\circ}$

$\angle D = \frac{5* 51.43^{\circ}}{2}$

$\angle D = \frac{257.15^{\circ}}{2}$

$\angle D = 128.57 ^{\circ}$

Hence:

$\angle D = \angle R = 128.57 ^{\circ}$

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