A radio isotope X with a half life 1.4 x 10⁹ years decays to Y which is stable

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:

No explanation available. Be the first to write the explanation for this question by commenting below.

admin:

View Comments (1)

  • 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

Related Questions

  1. 34 gram of water at 30⁰C is poured into a calorimeter at 15⁰C.
  2. If vₑ is escape velocity and vₙ is orbital velocity of a satellite
  3. Which is correct relation?
  4. Potentiometer measures the potential difference more accurately than a voltmeter
  5. Which two of the following five physical parameters have the same dimensions?