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The remainder is 2-p or 0.5p of the original amount.

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Q: What fraction of a radioactive nuclei remain after p half lives?
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After three half-lives what fraction of a radioactive sample will remain?

Approx 1/8 will remain.


What is the percentage of radioactive nuclei left after 3 half-lives have passed?

12.5%


What fraction of a radioactive sample remains after three half-lives?

Not sure what you mean by "had-lives". After 3 half lives, approx 1/8 would remain.


Why are the nuclei of elements with atomic numbers greater than 82 naturally radioactive?

Massive nuclei are unable to remain bound aganst the repulsive force of their protons, which all have positive charge. This also occurs with elements #43 (technetium) and #61 (promethium) which because of their particular nuclear geometry are inherently unstable and radioactive, with the only natural isotopes having half-lives of just over 2 years.


After three half-lives what fraction of a radioactive sample remains?

1/8 of the original amount remains.


What percentage of a radioactive element will remain after seven half lives?

After seven half lives, approximately 0.78125% (1/2^7) of the original radioactive element will remain. This can be calculated by repeatedly halving the remaining amount after each half life.


Why After three half-lives what fraction of a radioactive sample remains?

After three half-lives, only 1/8 (or 12.5%) of the original radioactive sample remains. This is because each half-life reduces the amount of radioactive material by half, so after three half-lives, you would have (1/2) * (1/2) * (1/2) = 1/8 of the original sample remaining.


How much of the radioactive element will be left one billion years from now?

It depends on the half-life of the radioactive element. After one billion years, only a fraction of the original amount would remain, based on the decay rate determined by the half-life of the element.


What percentage of a radioactive sample remains after 5 half-lives?

After 5 half-lives, 3.125% (or 1/2^5) of a radioactive sample remains. Each half-life reduces the sample by half, so after 5 half-lives, there is only a small fraction of the original sample remaining.


How much parent material will be left after five half-lives?

Only 1/32 of the original radioactive material will remain. (½)5 = 1/32


What fraction of U-238 atoms present at 1 half-life remain after 2 half-lives?

1/2 (50%) of them.


The range of half- lives of different radioactive elements is form?

From a tiny fraction of a second (10-18 seconds or so) to more than 1015 years.