A practical rule is that a radioactive nuclide is...

Name: Problem 11, Chapter 18: Chemistry
Uploaded: 2020-07-26T17:23:43-08:00
Duration: 1 min 45 s
Channel: Madi Sousa
Description: A practical rule is that a radioactive nuclide is essentially gone after 10 half-lives. What percentage of the original radioactive nuclide is left after 10 half-lives? How long will it take for 10 half-lives to pass for plutonium-239? Refer to Table 2.

A practical rule is that a radioactive nuclide is essentially gone after 10 half-lives. What percentage of the original radioactive nuclide is left after 10 half-lives? How long will it take for 10 half-lives to pass for plutonium-239? Refer to Table 2.

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which unstable atomic nuclei lose energy by emitting radiation. This transformation results in a change of the nucleus's composition and is governed by probabilistic laws, meaning that the decay of any given nucleus is random but statistically predictable for a large number of nuclei.

Half-Life

The half-life is the time required for half of the nuclei in a radioactive sample to decay. It is a characteristic constant for each radioactive nuclide and provides a convenient measure to understand the rate at which a substance decays over time.

Exponential Decay Law

The exponential decay law mathematically describes the process of radioactive decay, expressing the remaining quantity of a substance as an exponential function of elapsed time. Specifically, after n half-lives, the fraction remaining is given by (1/2)^n, which highlights the rapid decrease in the amount of a radioactive substance with time.

Percentage Remaining after Multiple Half-Lives

After a specific number of half-lives, the remaining percentage of the original substance can be calculated using the exponential decay formula. In the case of 10 half-lives, the remaining fraction is (1/2)^10, which equates to approximately 0.1% of the initial amount, demonstrating that the material is nearly fully decayed.

Time Scale Calculation for Radioactive Decay

Calculating the time scale for radioactive decay involves multiplying the half-life of the substance by the number of half-lives considered. This method is used to estimate the total duration over which a radioactive nuclide, such as plutonium-239, will effectively decay to an insignificant level after multiple half-lives.

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