Question

How many years are required for the amount of radium-226 on the remains of Madame Curie to reduce to 24.5% of the original amount, given that radium-226 has a half-life of 1600 years? Round the solution to the nearest whole number.

Answer 1

It would take approximately 6400 years for the amount of radium-226 on the remains of Madame Curie to reduce to 24.5% of the original amount.

Step-by-step explanation:

To determine the number of years required for the amount of radium-226 on the remains of Madame Curie to reduce to 24.5% of the original amount, we can use the concept of half-life. Radium-226 has a half-life of 1600 years, which means that every 1600 years, the amount of radium-226 is reduced by half.

Since we want to know when the amount will be 24.5% (or 0.245) of the original, we can use the formula: final amount = initial amount * (1/2)number of half-lives

Solving for the number of half-lives required, we get: number of half-lives = log0.5(final amount / initial amount)

Substituting the given values, we get: number of half-lives = log0.5(0.245 / 1)

Calculating this, we find that approximately 3.11 half-lives are required. Since we round up to the nearest whole number, it would take 4 half-lives or 6400 years for the amount of radium-226 to reduce to 24.5% of the original amount.