Question

If 18 g of a radioactive substance are present initially and 8 yr later only 9.0 g remain, how much of the substance, to the nearest tenth of a gram, will be present after 19 yr?

After 19 yr, there will be g of the radioactive substance.
(Do not round until the final answer. Then round to the nearest teath as needed.)​

Answer 1

Since the amount dropped to 1/2 of the initial amount over a period of 7 years, you can assume the half-life is 7 years.

m(t) = m0 (0.5)t/7,

t = years elapsed from the time the amount was m0

In grams,

m(t) = 8 (0.5)t/7

m(8) = 8 (0.5)8/7 g ≅ ? g

Step-by-step explanation:

Answer 2

To find out how much of the radioactive substance will be present after 19 years, we can use the concept of half-life. The half-life is the time it takes for half of the substance to decay. In this case, we are given that the half-life is 8 years. Since 8 years have passed, one half-life has occurred, meaning that only 9 g remain.

Step-by-step explanation:

To find out how much of the radioactive substance will be present after 19 years, we can use the concept of half-life. The half-life is the time it takes for half of the substance to decay. In this case, we are given that the half-life is 8 years.

Since 8 years have passed, one half-life has occurred, meaning that only 9 g remain. We can use this information to find the decay constant, which is the fraction of the substance that decays in one year.

The decay constant can be calculated by dividing the natural logarithm of 0.5 (since we are looking for the fraction that remains after one half-life) by the half-life. In this case, the decay constant is approximately 0.0866.

Now, we can use the decay constant to find the amount of substance remaining after 19 years. We can use the formula:

Remaining amount = Initial amount * e^(- decay constant * time)

Plugging in the given values, we have:

Remaining amount = 18 g * e^(- 0.0866 * 19)

Calculating this, we find that after 19 years, approximately 4.6 g of the radioactive substance will remain.