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Analysis of potassium and argon atoms in...

Analysis of potassium and argon atoms in a moon rock sample by a mass spectrometer shows that the ratio of the number of stable `Ar^(40)` atoms present to the number of radioactive `K^(40)` atoms is 7 : 1 . Assume that all the argon were produced by the decay of potassium atoms, with a half-life of `1.25 xx 10^(9)` year. How old is the rock?

A

`1.25 xx 10^(9) yr`

B

`3.75 xx 10^(9) `yr

C

`8.75 xx 10^(9)` yr

D

`1.00 xx 10^(10) ` yr

Text Solution

Verified by Experts

The correct Answer is:
B

Numberof atoms after time t `N_(0) -x` x
But from question, `(N_(0)-x)/x =1/7`
`x = 7/8 N_(0)`
`therefore (N_(0)-x) = N_(0)/8`
`N_(0) to N_(0)/2 to N_(0)/4 to N_(0)/8)`
So, time = `3 xx T_(1//2) = 3.75 xx 10^(9)` year
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