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Sagot :
The rate at which radioactive substances disintegrate is a constant for a
given radioactive material.
- The fossil is 710 million years old.
Reasons:
The half-life of a radioactive material is the time it takes half of the nucleus
of a radioactive material to disintegrate into other forms of materials
through the given off of energy and particles.
The half life of Uranium 235 = 710 million years
The product of the decay of Uranium 235 = Lead 207
The mass of Uranium 235 in the fossil = 4 micrograms
The mass of Lead 207 in the sample = 4 micrograms
Therefore, the mass of Lead 207 in the fossil is equal to the mass of
Uranium 235, therefore, a minimum of half of the Uranium 235 has
decomposed, which gives;
The time of decomposition of the Uranium 235 = 1 Half life = 710 million years
The age of the fossil = The time in which the Uranium has been
decomposing = The time of decomposition = 1 half life of Uranium 235 = 710
million years
- The age of the fossil = 710 million years
Using the formula for half-life, we get;
[tex]\displaystyle N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}[/tex]
The fossil contains initially only Uranium 235 with a minimum mass of 4 mg
+ 4 mg = 8 mg, which gives;
N₀ = 8 mg
N(t) = The current mass of Uranium 235 = 4 mg
[tex]\displaystyle t_{1/2}[/tex] = 710 million years
[tex]\displaystyle 4 = 8 \cdot \left (\dfrac{1}{2} \right )^{\dfrac{t}{710}[/tex]
[tex]\displaystyle \frac{4}{8} = \frac{1}{2} = \left (\dfrac{1}{2} \right )^{\dfrac{t}{710}[/tex]
Therefore;
[tex]\displaystyle \left( \frac{1}{2}\right)^1 = \left (\dfrac{1}{2} \right )^{\dfrac{t}{710}[/tex]
[tex]\displaystyle 1 = {\dfrac{t}{710}[/tex]
t = 710
- The age of the fossil, t = 710 million years
Learn more here:
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