An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain?
2. A 2.5 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific Test Site. The half-life of the radioactive element is 28 years. How much of this element will remain after 112 years? 0.15625g remains
3. An element has a half-life of 29 hours. If 100 mg of the element decays over a period of 58 hours, how many mg of the element will remain?

Hey there!

A half-life means after a certain amount of time, half of that substance will be gone/changed after that time.

1.

There are 3 half-lives in 90 years because 90 ÷ 30 = 3.

So, we divide the 1mg sample in half 3 times.

1 ÷ 2 = 0.5

0.5 ÷ 2 = 0.25

0.25 ÷ 2 = 0.125

There will be 0.125mg of the radioactive sample remaining after 90 years.

2.

There are 4 half-lives in 112 years because 112 ÷ 28 = 4  

So, we divide the 2.5g sample in half 4 times.

2.5 ÷ 2 = 1.25

1.25 ÷ 2 = 0.625

0.625 ÷ 2 = 0.3125

0.3125 ÷ 2 = 0.15625

There will be 0.15625g of the radioactive sample remaining after 112 years.

3.

There are 2 half-lives in 58 hours because 58 ÷ 29 = 2.

So, over the period of 2 half-lives 100g decays.

We can just divide 100g in half twice to demonstrate the two half-lives.

100 ÷ 2 = 50

50 ÷ 2 = 25

So, there is 25 grams left of the radioactive substance left after 58 hours.

Hope this helps!

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