The half-life of radium-226 is 1600 years, which means that every 1600 years, half of the initial amount of radium-226 will decay.
To calculate the amount of radium-226 remaining after 4800 years, we can determine the number of half-lives that have elapsed in that time period. Since 4800 years is three times the half-life of radium-226 (1600 years), three half-lives have occurred.
After each half-life, the amount of radium-226 remaining is halved. So, after three half-lives, the remaining amount will be (1/2) x (1/2) x (1/2) = 1/8 of the original amount.
Therefore, the amount of radium-226 remaining after 4800 years would be:
Remaining amount = (1/8) x Initial amount
Given that the initial amount is 1000 grams, we can calculate the remaining amount as follows:
Remaining amount = (1/8) x 1000 grams = 125 grams
So, after 4800 years, approximately 125 grams of radium-226 would be left out of the initial 1000 grams.