Question

A certain element has a half life of 2.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 45​% of the original element​ remains; the other 55​% decayed into lead. How old is the​ rock? b. Analysis of another rock shows that it contains 65​% of its original​ element; the other ​35% decayed into lead. How old is the​ rock?

Answer 1

Explanation:

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

fraction remaining = 55% = 0.55

0.55 = 0.5n

log 0.55 = n log 0.5

-0.2596 = -0.301 n

n = 0.8625 = # of half lives elapsed

0.8625 half lives x 2.5 billion years/half live = 2.16 billion years have elapsed = age of the rock

b) 0.15 = 0.5n

log 0.15 = n log 0.5

-0.824 = -0.301 n

n = 2.74 half lives

2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock