When does a given radioactive material like radium 226 cease to be radioactive?

A radioactive material like radium-226 ceases to be radioactive when it has fully decayed and no longer emits radiation. This process is measured in terms of half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.

Here are the steps to understand when a given radioactive material like radium-226 ceases to be radioactive:

1. Identify the half-life of the radioactive material: The half-life of radium-226 is about 1,600 years. This means that after 1,600 years, half of the radium-226 in a sample will have decayed into other elements.

2. Understand the decay process: Radium-226 decays by alpha decay into radon-222. This process continues with the radon-222 decaying into other elements, and so on, until a stable element is reached. In the case of radium-226, the final stable element is lead-206.

3. Calculate the time for full decay: It's important to note that radioactive decay is a probabilistic process. Even after many half-lives, there will still be a small number of radioactive atoms remaining. However, for practical purposes, it's often said that a sample is no longer radioactive after about 10 half-lives. So, for radium-226, this would be approximately 16,000 years.

4. Consider the implications: While the radioactivity of the sample decreases over time, it does not mean that the material is safe to handle. The decay products of radium-226, such as radon gas, are also radioactive and can pose health risks.

So, a given radioactive material like radium-226 ceases to be radioactive when it has fully decayed into stable elements, which for practical purposes, is typically after about 10 half-lives, or approximately 16,000 years in the case of radium-226.