A radio active substance has a half-life of 2 hours. How much of the substance will remain after 6 hours have passed?

Answer 1

So a substance's half-life is how long it takes for the initial amount to reduce by 50%.

Since the half life is 2 hours, and it asks about the amount 6 hours later, we can say we know 3 half lives have occurred. (6 hours [total time since radioactive decay started to the time we are currently interested in] divided by 2 hours [how long each half life is] gives us that three half lives have occurred.

So if we think of a substance having 100 units originally and it has a half life of 2 hours. After two hours(one half life), 50 units will remain because 100(0.5)=50. So now, we have 50 units as our initial, so when another 2 hours passes (so a total of four hours) we have 25 units left because 50(0.5)=25. Finally, for the the last 2 hours (the third half life), the 25 units is reduced by 50%, yielding 12.5 units.

so 12.5 units is the answer if we assume there were 100 units initially. Luckily, we can think of our units as percent! So we have 12.5 % of the original amount. Switching between units and percents makes sense because at the beginning, we have 100 units, aka 100 percent of the original!

This was to demonstrate how the logic goes. But you can also just use this, which is conveying this logic through the formula

final amount= original amount * (0.5 ^{amount of half lives)} )

12.5= 100 * (0.5³)

Answer 2

Each 2 hours, half of the substance breaks down into something else. So, after 2 hours, 50% is left. And after 4 hours, 25% is left. And after 6 hours, 12.5% is left.

Answer 3

With a half-life, you multiply by 1/2 every half-life time period.

So, if the half-life is two hours, you multiply the amount of the substance by 1/2.

So, after two hours you would have 1/2 of the original amount of substance (1 multiplied by 1/2). We are assuming one since they haven’t given how much of the original substance there is.

After four hours you would have 1/4 of the original amount of substance (1/2 times 1/2).

After six hours you would have 1/8 of the original amount of substance (1/4 times 1/2).

1/8, or 12.5%, is your answer!

There's also an equation: Final Amount = Original Amount * (0.5 ^{(amount of half lives)} )

12.5 = 100 * (0.5³)

Amount of half lives is amount of time/length of half-life.