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The half life of Pb-210 is 22 years. A decayed animal shows 25% of the original Pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?

User Bettyanne
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This is an easy half-life calculation. (Most of these are NOT easy).
If 25% remains of an original amount of 100%, then the time elapsed is precisely 44 years. (2 half-lives)
In 22 years (one half-life), it would be 50%
In 44 years (two half-lives), it would be 25%
In 66 years (three half-lives), it would be 12.5%
In 88 years (four half-lives), it would be 6.25%


User Eugene Kulabuhov
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8.3k points
3 votes

Answer:

44 years.

Explanation:

Let original amount be 100.

We have been given that the half life of Pb-210 is 22 years. A decayed animal shows 25% of the original Pb-210 remains.

We will use half-life formula to solve our given problem.


A=a\cdot (0.5)^{(t)/(h)}, where,

A = Amount after t units of time,

a = Initial amount,

t = Time,

h = Half-life.


25=100\cdot (0.5)^{(t)/(22)}


(25)/(100)=\frac{100\cdot (0.5)^{(t)/(22)}}{100}


0.25=(0.5)^{(t)/(22)}

Take natural log of both sides:


\text{ln}(0.25)=\text{ln}((0.5)^{(t)/(22)})

Using natural log property
\text{ln}(a^b)=b\cdot \text{ln}(a), we will get:


\text{ln}(0.25)=(t)/(22)*\text{ln}(0.5)


\frac{\text{ln}(0.25)}{\text{ln}(0.5)}=\frac{t*\text{ln}(0.5)}{22*\text{ln}(0.5)}


(-1.38629436)/(-0.69314718)=(t)/(22)


2=(t)/(22)


2*22=(t)/(22)*22


44=t

Therefore, the animal has been deceased to 44 years.

User Horsh
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9.0k points
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