The time since the rock reached its closure temperature is 289.8 years.
When the rock was discovered, it would contain 4.375 g of Europium 151.
If the number of atoms of samarium 151 at its closure temperature is N₀ and if it had N atoms when discovered, then,
[tex]\frac{N}{N_0} =\frac{1}{2^n}[/tex]
here, n is the number of half lives.
The mass of the isotope is proportional to the number of its atoms present in the sample. hence substitute 0.625 g for N and 5 g for N₀.
[tex]\frac{N}{N_0} =\frac{1}{2^n}\\ \frac{0.625g}{5 g} =\frac{1}{8} =\frac{1}{2^3}[/tex]
hence, the number of half live n is equal to 3.
If the half life of the isotope Samarium is 96.6 years, then the time that has elapsed from time it reaches its closure temperature and its discovery is given by,
[tex]t=3*96.6 years=289.8 years.[/tex]
Since Samarium decays to Europium, the mass of Europium at the time of discovery is equal to the mass of Samarium that has decayed.
The mass of Europium 151 at the time of discovery is given by,
[tex]m=(5g)-(0.625g)=4.375g[/tex]
Thus,the time since the rock reached its closure temperature is 289.8 years and when the rock was discovered, it would contain 4.375 g of Europium 151.
Answer:
The time since the rock reached its closure temperature is 289.8 years.When the rock was discovered, it would contain 4.375 g of Europium 151.
Explanation:
