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A radio isotope X with a half life 1.4 x 10⁹ 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
Options
(a) 1.96 x 10⁹ years
(b) 3.92 x 10⁹ years
(c) 4.20 x 10⁹ years
(d) 8.40 x 10⁹ years
Correct Answer:
4.20 x 10⁹ years
Explanation:
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X/Y=1/7
Y=7X
Let the initial atoms be N.
Then,
X+Y=N
X+7X=N
8X=N
X=N/8
Hence, the final atoms be N/8.
N/8/N=(1/2)^n
(1/8)^3=(1/2)^n
n=3
Then, t=n×T1/2
t=3×1.4×10^9
t=4.2×10^9