Question

1. The half-life of carbon-14 is 5730 years. A sample is found to have one-eighth the original amount of carbon-14 in it. How old is the sample?

5730 years, 716 years, 45800 years, 17200 years

2. Why wouldn't you use carbon-14 dating on a piece of shell that was estimated to be 1 million years old?

Sea shells do not have radioisotopes, carbon dating is only useful on plants, uranium dating is better for items older than 1/2 million years, carbon dating can only be used on items that were once alive, the amount of radioactive carbon in the sample would probably be too small to measure

3. The isotope Cesium-137, which has a half-life of 30 years, is a product of nuclear power plants. how long will it take for this isotope to decay to about one-sixteenth its original amount?

480 years, 240 years, 120 years, 960 years

Answer 1

Question 1

The reaction follows first order reaction. Let us calculate the rate constant

Rate constant = 0.693 / Half life

Rate constant = 0.693 / 5730 Year = 1.209 x10^-4 year^-1

Then we can use the following formula to calculate how old the sample is

ln A = -kt + ln A_o

k = rate constant                   t = time

Ao = Initial concentration                A = concentration at time t

A = 1/ 8 = 0.125 A_o = 1

k =   1.209 x10^-4 year^-1

ln 0.125= -1.209 x10^-4 year^-1 x t + ln 1

-2.0798 / -1.209 x10^-4 year^-1 = t

t = 17200 year .

Hence the sample is 17200 years old

Question 3

Rate constant = 0.693 / Half life

Rate constant = 0.693 / 30 Year = 0.0231year^-1

A = 1/ 16 = 0.0625 A_o = 1

k =   0.0231 year^-1

ln 0.0625= -0.0231 year^-1 x t + ln 1

-2.7730 / -0.0231  year^-1 = t

t = 120 year .

Hence the sample is 120 years old