Questions: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 3000 years? mg Give your answer accurate to at least 2 decimal places.

Solution Steps

The half-life of a substance is the time it takes for half of the sample to decay. For Radium-226, the half-life is 1590 years. This means that every 1590 years, the amount of Radium-226 will reduce to half of its initial amount.

Calculate how many half-lives have passed in 3000 years. This is done by dividing the total time period by the half-life of the substance: \[ \text{Number of half-lives} = \frac{3000 \text{ years}}{1590 \text{ years/half-life}} \]

Use the formula for exponential decay based on half-lives: \[ \text{Remaining amount} = \text{Initial amount} \times \left(\frac{1}{2}\right)^{\text{Number of half-lives}} \] Substitute the initial amount (300 mg) and the number of half-lives calculated in Step 2 into the formula to find the remaining amount of Radium-226 after 3000 years.

Final Answer