Question

Radioactive decay of 40K atoms in an igneous
rock has resulted in a ratio of 25 percent 40K
atoms to 75 percent 40Ar and 40Ca atoms.
How many years old is this rock?
(1) 0.3 10^9 y (3) 2.6 10^9 y
(2) 1.3 10^9 y (4) 3.9 10^9 y

Answer 1

Radioactive decay of 40K atoms in an igneous rock has resulted in a ratio of 25 percent 40K atoms to 75 percent 40Ar and 40Ca atoms. this rock 2.6 10^9 y years old. The answer is number 3. The rest of teh choices do not answer the question above.

Answer 2

The age of the rock is mathematically given as

t= 2.6 10^9 y

What is the age of the rock?

Question Parameter(s):

a ratio of 25 percent 40K

atoms to 75 percent 40Ar and 40Ca atoms.

Generally, the equation for the half lif  is mathematically given as

$t= \frac{ t_{ \frac{1}{2} } }{ln(2)} ln( \frac{ K_{f} + \frac{ Ar_{f} }{0.109} }{ K_{f} } )$

Therefore

$t= \frac{1.251* 10^{9} }{ln(2)} ln( \frac{0.25+ \frac{0.75}{0.109} }{0.25} )$

t= 2.6 10^9 y

In conclusion,  the age of the rock is

t= 2.6 10^9 y

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