The decay of potassium-40 to argon-40 can be used to date igneous rocks because of its long half-life. An igneous rock just formed does not contain argon gas and the gas formed in decay are trapped inside the rock. A rock sample contains potassium-40 and argon-40 in the ratio 1: 15. How many half-lives of potassium-40 have elapsed?
Answer is 4.
Can anyone help me to explain how to calculate ? Thx for helping!
Atomic physics
2007-04-14 7:34 am
回答 (2)
2007-04-14 8:09 am
✔ 最佳答案
After each half-life, the proportion of K in the mixture is 1/2 times the original proportion.At present, the ratio of K in the mixture 1 : 15+1 = 1 : 16 , i.e. the proportion of K in the mixture is 1/16.
Let x be the no. of half-life.
(1/2)^x = 1/16
x = 4
2007-04-14 8:23 am
Let m kg be the original mass of K-40 on the rock samle,
since after decay, there is m/16 kg left and 15m/16 kg have been decayed to Ar-40
thus, m/2^n = m/16 where n is the no of half-lives lapsed
i.e. 2^n = 16
solving for n gives =4
since after decay, there is m/16 kg left and 15m/16 kg have been decayed to Ar-40
thus, m/2^n = m/16 where n is the no of half-lives lapsed
i.e. 2^n = 16
solving for n gives =4
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