A certain element has a half life of 3.5 billion years. a. You find a rock conta

Question

A certain element has a half life of

3.5

billion years. a. You find a rock containing a mixture of the element and lead. You determine that

40%

of the original element remains; the other

60%

decayed into lead. How old is the rock?b. Analysis of another rock shows that it contains

5%

of its original element; the other

95%

decayed into lead. How old is the rock?

a. The rock is approximately

________

billion years old.

(Round to one decimal place as needed.)

b. The rock is approximately

________

billion years old.

(Round to one decimal place as needed.)

Explanation / Answer

Solution

(a) For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.

fraction remaining = 40% = 0.40

0.40 = 0.5n

log 0.40 = n log 0.5

n = 1.3219 of half lives elapsed

1.3219 half lives x 3.5 billion years/half live = 4.6 billion years have elapsed = age of the rock

(b) 0.05 = 0.5n

ln(0.05)=nln(0.5)

n = 4.3219

4.3219 half lives x 3.5 billion years/half live = 15.1 billion years have elapsed = age of the rock

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