Question

while carbon - 14 can be useful for determining the age of a fossil, it has two primary shortcomings
1 it decays quickly, so after about ______ years, it is no longer an accurate measure of age.

1. it is useful only for dating objects that were once ______

geologists can resolve these limitations by using other isotopes, such as ____ which has a half - life of ____ years.
when decay begins
for an organism, the amount of unstable isotope (carbon - 14) it contains no longer changes when the organism dies.
for rocks inside earths mantle, the extreme heat allows isotopes to diffuse in and out of the minerals within the rock. as the rock reaches the crust and begins to cool, it approaches what is called the ______. at this temperature, isotopes stop diffusing and the amount of unstable isotope no longer changes.
so, using the proportion of unstable isotope to daughter isotope, scientists can calculate the amount of time that has passed from a minerals closure temperature or an organisms death.
the isotope nickel - 63 decays into copper - 63, with a half - life of 100 years. suppose that a rock contains 4 grams of nickel - 63 when it reaches its closure temperature and 0.25 grams when it is discovered. how long has it been since the rock cooled to its closure temperature?
step 1: how many half - lives have occurred? step 2: how many years is that?

therefore, ______ years must have passed since the sample reached its closure temperature.

Explanation:

Step1: Calculate the number of half - lives

We know that the initial mass of nickel - 63 \(N_0 = 4g\) and the final mass \(N=0.25g\). The formula for the amount of a radioactive substance remaining after \(n\) half - lives is \(N = N_0\times(\frac{1}{2})^n\).
Substitute \(N_0 = 4\) and \(N = 0.25\) into the formula:
\(0.25=4\times(\frac{1}{2})^n\)
\(\frac{0.25}{4}=(\frac{1}{2})^n\)
\(0.0625 = (\frac{1}{2})^n\)
Since \(\frac{1}{16}=0.0625\) and \(\frac{1}{16}=(\frac{1}{2})^4\), then \(n = 4\)

Step2: Calculate the time passed

Given that the half - life \(T = 100\) years.
The time \(t\) passed is given by the formula \(t=n\times T\)
Substitute \(n = 4\) and \(T = 100\) into the formula:
\(t=4\times100\)
\(t = 400\)

Answer:

400