Question

The half-lives for the radioactive decay of various elements are listed in the table below.

Parent Isotope Daughter Isotope Half life
Carbon-14 Nitrogen-14 5,730
Uranium-235 Lead-207 710 million
Potassium-40 Argon-40 1.25 billion

Required:
a. Suppose you discovered a meteorite that contains a small amount of potassium-40 and its decay product argon-40. You determine that 1/8 of the original potassium-40 remains; the other 7/8 has decayed into argon-40. How old is the meteorite?
b. A piece of cloth was painted with organic dye 40,110 years ago. What percentage of the original carbon-14 in the organic dye remains after all this time?
c. The oldest minerals found on Earth are zircons. One isotope used to measure their age is uranium-235. A single crystal contained 200 nanograms of uranium-235 when it first formed. How much uranium-235 does the crystal still contain if it formed 4.26 billion years ago?
d. Is radiocarbon dating a useful tool for determining the age of the solar system? Explain why or why not

Answer 1

See solution and explanation below

Step-by-step explanation:

a) From;

N/No = (1/2)^t/t1/2

1/8 = (1/2)^t/1.25 * 10^9

(1/2)^3 = (1/2)^t/1.25 * 10^9

3 = t/1.25 * 10^9

t = 3 * 1.25 * 10^9

t = 3.75 * 10^9 years

b)

N/No = (1/2)^40,110/5,730

N/No = (1/2)^7

N/No = 1/128

percentage remaining after 40,110 years = 1/128 * 100 = 0.78%

c) N/200 * 10^-9 = (1/2)^4.26 * 10^9/0.710 * 10^9

N/200 * 10^-9 = (1/2)^6

N/200 * 10^-9 = 1/64

64 N = 200 * 10^-9

N= 3.125 * 10^-9 g

d) Radiocarbon dating can not be used to determine the age of the solar system since the solar system is as old as the universe and was formed billions of years ago. Radiocarbon dating can only be accurately used to obtain the age of objects of plant or animal origin between 1000 - 10000 years old.