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# Half-life.......

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A radioactive element has a half-life of h years. In 500,000 years a given amount of this element would decay to 10% of its original amount. What is the half-life of this element? Thanks for help.

Guest Apr 2, 2017
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### 2+0 Answers

#1
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Use N/N0 = e^-(ln2*t/h)

0.1 = e^-(ln2*500000/h)

ln0.1 = -ln2*500000/h

h = -ln2*500000/ln0.1 ≈ 150515 years

.

Alan  Apr 2, 2017
edited by Alan  Apr 2, 2017
#2
+1

Also, by this simple method:

0.1 = 2^-(500,000/h)

1/10 = 2^-(500,000/h) take the reciprocal of both sides,

10 = 2^(500,000/h)       take the log of both sides

500,000/h =log(10) / log(2)

500,000/h =3.321928...

h =500,000 / 3.321928

h ~ 150,515 years - the half-life of this element.

Guest Apr 2, 2017

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