Answer:
The half-life of the isotope is 3.75 × 10⁴ years.
Explanation:
Hi there!
The half-life of the radioactive isotope is the time at which half of the atoms of the sample decay.
The sample has 6.00 × 10⁷ atoms and every year 8.00 × 10² of them decay. Then, we have to find the time at which 30 million atoms decay:
If 8.00 × 10² atoms decay per year, 3.00 × 10⁷ atoms will decay in:
3.00 × 10⁷ atoms · ( 1 year / 8.00 × 10² atoms) = 3.75 × 10⁴ years
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Half-life is the time needed to decay the half number of nuclei. The half-life of the isotope is 37,500 years.
Half-life is the time needed to decay the half number of nuclei.
We know that the initial number of the nucleus is 60 million, while the decay rate is 800 nuclei/year. Since we need to find the half-life of the radioactive isotope, therefore, we need to find the time when only 30 million nuclei are left.
Thus, we need to find the time that will be needed in order to decay 30 million nuclei.
[tex]\dfrac{30 \times 10^6\rm\ Nuclei}{800\rm\ Nuclei/year} = 37,500\rm\ year[/tex]
Hence, the half-life of the isotope is 37,500 years.
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