Question

If 10g of a radioactive substance are present initially and 3 years later only 5 g remain, how much of the substance will be present in 5 years

Answer 1

Answer:

The mass of the substance that will remain after 5 years is 3.15 g

Step-by-step explanation:

Given;

initial mass of the radioactive substance, a = 10 g

remaining mass after 3 years, y = 5g

Generating a half-life equation;

$y = ab^x\\\\5 = 10b^3\\\\\frac{5}{10} = b^3\\\\0.5 = b^3\\\\log(0.5) = log(b^3)\\\\3log(b) = log(0.5)\\\\log(b) = \frac{1}{3} log(0.5)\\\\log(b) = log(0.5)^{\frac{1}{3}} \\\\b = 0.5^{\frac{1}{3}} \\\\b = 0.7937\\\\y = 10(0.7937)^x$

After 5 years, the mass of the substance that will be present is given by;

y = 10(0.7937)⁵

y = 3.15 g

Therefore, the mass of the substance that will remain after 5 years is 3.15 g