the half - life of radium is 1690 years. if 60 grams are present now, how much will be present in 550 years?

Explanation:

Step1: Identify decay - formula

The radioactive - decay formula is $A = A_0(\frac{1}{2})^{\frac{t}{T}}$, where $A_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half - life.

Step2: Substitute values

Given $A_0 = 60$ grams, $t = 550$ years, and $T = 1690$ years. Substitute into the formula: $A=60\times(\frac{1}{2})^{\frac{550}{1690}}$.

Step3: Calculate exponent value

First, calculate $\frac{550}{1690}\approx0.325444$. Then, $(\frac{1}{2})^{0.325444}=2^{- 0.325444}$. Using a calculator, $2^{-0.325444}\approx0.7937$.

Step4: Calculate final amount

Multiply by the initial amount: $A = 60\times0.7937 = 47.622$ grams.

Answer:

$47.622$ grams