Final answer:
To find the mass that will remain after 1000 years, we can use the formula for exponential decay. The mass that will remain can be calculated using the given formula.
Step-by-step explanation:
To find the mass that will remain after 1000 years, we can use the formula for exponential decay:
Final mass = Initial mass × (1/2)^(number of half-lives)
Since the half-life of radium-226 is 1590 years, we calculate the number of half-lives as:
number of half-lives = 1000 years / 1590 years = 0.6283 (approximately)
Substituting the values into the formula:
Final mass = Initial mass × (1/2)^0.6283
Therefore, the mass that will remain after 1000 years can be calculated using the given formula.