niobium - 91 has a half - life of 680 years. after 2,040 years, how much niobium - 91 will remain from a…

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{t}{T_{1/2}}$, where $t = 2040$ years and $T_{1/2}=680$ years. So $n=\frac{2040}{680}=3$.

Step2: Use radioactive decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0 = 300.0$ g and $n = 3$. Then $N=300\times(\frac{1}{2})^3$.

Step3: Calculate remaining amount

$N = 300\times\frac{1}{8}=37.5$ g.

Answer:

37.5 g