Nuclear Physics and RadioactivityHard
Question
Mass spectrometric analysis of potassium and argon atoms in a Moon rock sample shows that the ratio of the number of (stable) 40Ar atoms present to the number of (radioactive) 40K atoms is 10.3. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of 1.25 × 109 yr. How old is the rock :-
Options
A.2.95 × 1011 yr
B.2.95 × 109 yr
C.4.37 × 109 yr
D.4.37 × 1011 yr
Solution
19K40 → 20Ar40 + -1e0 + 
(N0) (0)
(N1) (N2 = N0 - N1)
given
= 10.3 ⇒ 
= 10.3
⇒
= e-λt
⇒t = ln11.3
⇒t = 4.37 × 109 yrs
(N0) (0)
(N1) (N2 = N0 - N1)
given
= 10.3 ⇒ = 10.3⇒
= e-λt⇒t = ln11.3
⇒t = 4.37 × 109 yrs
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