Final answer:
To determine the age of a rock based on the remaining amount of a radioactive element, we use the half-life of that element. Assuming a logarithmic decay, measurement of remaining element and decay products allows for age estimations, such as calculating a rock to be approximately 1.7 billion years old based on the decay of Rb-87 to Sr-87.
Step-by-step explanation:
If you started with 100 lokium cubes and now have only 12 left, we can use principles of radioactive decay to estimate the age of the rock. Lokium is a fictional element, but let's assume it decays in a manner similar to real radioactive elements. The decay of a radioactive element is generally logarithmic, and its rate can be characterized using its half-life—the time it takes for half of the element to decay. Without the actual half-life of lokium, we cannot directly calculate the age. However, real-world examples such as Rb-87 that decays to Sr-87 with a known half-life of 4.7 x 10ⁱ⁰ years can help us estimate that the rock is approximately 1.7 billion years old. This calculation assumes that the original amount of Rb-87 was known, and by measuring the current amount along with the decay product Sr-87, the age can be calculated using decay formulas.
Another example is hydrogen-3 (tritium) which has a half-life of 12.3 years. To determine the time for 99.0% of a sample to decay, multiple half-lives must be computed as the sample decreases exponentially. In real-world decay scenarios, other elements with much shorter half-lives like plutonium may also be found, but their presence would be more indicative of recent activity since their half-lives are too short to date back to the formation of the Earth.
Therefore, when it comes to estimating the age of rocks or archaeological finds, half-life is an essential concept in understanding how much time has passed based on the proportions of undecayed radioactive material and its decay products.