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babymother [125]
3 years ago
7

226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?

Mathematics
1 answer:
Ray Of Light [21]3 years ago
8 0
\bf \textit{Amount for Exponential Decay using Half-Life}\\\\
A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &10\\
t=\textit{elapsed time}\to &1000\\
h=\textit{half-life}\to &1599
\end{cases}
\\\\\\
A=10\left( \frac{1}{2} \right)^{\frac{1000}{1599}}
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A negative exponent means the number of the exponent divide by the number. The the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

Given information-

The radius of a nitrogen atom is 5.6\times10^{-11} meters.

The radius of a beryllium atom is 1.12 \times10^{-10} meters

<h3>Negative exponents</h3>

A negative exponent means the number of the exponent divide by the number.

As the radius of the nitrogen atom is 5.6\times10^{-11} meters. Convert it in the power of negative exponent of 10.

Let the radius of the nitrogen is r mm. Thus,

r=5.6\times 10^{-11}\\&#10;r=5.6\times 10^{-10-1}\\&#10;r=5.6\times 10^{-10}\times10^{-1}\\&#10;r=\dfrac{5.6\times 10^{-10}}{10} \\&#10;r=0.56\times 10^{-10}

Now the base of the exponents of both the atoms are same. As the radius of the nitrogen atom is 0.56\times 10^{-10} meters and the radius of the beryllium atom is 1.12 \times10^{-10}. Thus the radius of beryllium atom is larger.

To calculate how many times, the radius of beryllium atom should be divided by the radius of a nitrogen atom. Thus,

=\dfrac{1.12\times10^{-10}}{0.56\times10^{-10}} \\&#10;=2

Thus the the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

Learn more about the negative exponents here;

https://brainly.in/question/1221452

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Answer:

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So Frog 2 = 3 yards

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It won by 3 - 2.75 = 0.25 Yards

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