The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 940 years? 56.57 grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

To find out how much radium will be present in 940 years, we can use the half-life formula. The formula is: \[ N = N_0 \times \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \] Where: - \( N_0 \) is the initial amount of substance (80 grams), - \( t \) is the time passed (940 years), - \( t_{1/2} \) is the half-life (1690 years). Plugging the numbers in: 1. Calculate \( \frac{t}{t_{1/2}} \): \[ \frac{940}{1690} \approx 0.555 \] 2. Then calculate how much of the radium remains: \[ N \approx 80 \times \left( \frac{1}{2} \right)^{0.555} \] \[ N \approx 80 \times 0.759 \approx 60.724 \] So, after rounding to the nearest thousandth, approximately **60.724 grams** of radium will be present after 940 years.