potassium - 40 has a half - life of 1.277×10^9 years. after 1.022×10^10 years, how much potassium - 40 will…

Explanation:

Step1: Calculate number of half - lives

The formula for the number of half - lives $n=\frac{t}{T_{1/2}}$, where $t$ is the time elapsed and $T_{1/2}$ is the half - life. $n=\frac{1.022\times 10^{10}}{1.277\times 10^{9}}=\frac{1.022}{1.277}\times10\approx 8$

Step2: Use decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount and $N$ is the remaining amount. $N = 500.3\times(\frac{1}{2})^8$ $N = 500.3\times\frac{1}{256}\approx 1.95$ g

Answer:

Approximately 1.95 g