Arock outcrop was found to have 95.82% of its parent u- 238 isotope remaining. approximate the age of the outcrop. the half-life of u- 238 is 4.5 billion years old.
a) 277 million years
b) 1.7 billion years
c) 14 million years
d) 21 million years

A) 277 million years

Step-by-step explanation:

Here, decay of U-238 is first order reaction. (since most of the nuclear decays are first order).

so, the equation t = × ln()

where, t = time from start of reaction

           k = reaction constant

           A(0) = initial concentration; A = present concentration.

     ⇒ 4.5 billion = 4500 million years = × ln2.

Now, given 95.82% of parent U-238 isotope is left.

⇒ t = × ln()

  t = × ln()

⇒ t ≅ 277 million years.

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