Questions: Nobelium, an element discovered in 1958, has a half-life of 10 min under certain conditions. In a sample containing 1 g of nobelium, the amount left after t min is given by A(t)=(0.5)^(t / 10). (Round to three decimal places.) (a) How much nobelium is left after 9 min? (b) How much nobelium is left after 1 h?

Solution Steps

We are given the decay formula for nobelium, \( A(t) = (0.5)^{t / 10} \), where \( t \) is the time in minutes. We need to find the amount of nobelium left after 9 minutes and after 1 hour.

To find the amount of nobelium left after 9 minutes, we substitute \( t = 9 \) into the decay formula: \[ A(9) = (0.5)^{9 / 10} \] Using a calculator, we find: \[ A(9) \approx (0.5)^{0.9} \approx 0.5359 \] Since the initial amount is 1 g, the amount left is: \[ 1 \times 0.5359 = 0.5359 \text{ g} \]

To find the amount of nobelium left after 1 hour (which is 60 minutes), we substitute \( t = 60 \) into the decay formula: \[ A(60) = (0.5)^{60 / 10} = (0.5)^6 \] Using a calculator, we find: \[ (0.5)^6 = 0.015625 \] Since the initial amount is 1 g, the amount left is: \[ 1 \times 0.015625 = 0.0156 \text{ g} \]

Final Answer