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In nature, some radioactive compounds exist, but later decay to more stable nuclei. Radioactive dating is achieved by assessing the ratio of a target nucleus to its radioactive decline component with a known half-life. In this case, the age of a certain material, or rocks, can be calculated by comparing the usual atmospheric ratio of Lu-Hf with that of the sample. The reason this works is that because the nuclei's half-life is calculated, you can calculate how many half-lives have passed by calculating how relatively reduced the sum of radioactive nuclei is to the product.
