Question 530: Atoms & Nuclei

Question

A radioactive X with a half life 1.4 $$ 	imes $$ 10
9
years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

Accepted Answer

Using N = N
0
e
Ã¢ÂÂÃÂ»t
Now 1 = 8e
Ã¢ÂÂÃÂ»t
or, $${1 \over 8}$$ = e
Ã¢ÂÂ (ln 2/T)t
or, $${\left( {{1 \over 2}} \right)^3}$$
 = (2)
Ã¢ÂÂt/T
or, t/T = 3
Now time, t = 3 ÃÂ 1.4 ÃÂ 10
9
= 4.2 ÃÂ 10
9
years

Answer

1.96 $$ 	imes $$ 10
9
years

Answer

3.92 $$ 	imes $$ 10
9
years

Answer

4.20 $$ 	imes $$ 10
9
years

Answer

8.40 $$ 	imes $$ 10
9
years

Atoms & Nuclei

A radioactive X with a half life 1.4 $ \times $ 10 9 years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

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