D. One eight
12.5%
If I take a radioactive sample of 400 moles of an unknown substance and let it decay to the point of three half-lives I would have 50 moles left of the sample. 1/2 of what is left will decay in the next half-life. At the end of that half-life I will have 25 moles left of the unknown substance or 4/25.
When three-quarters of a radioactive isotope has decayed, it means that 1/4 (or 25%) of the original isotope remains. This corresponds to 2 half-lives, because each half-life halves the amount of radioactive material remaining.
Half of a radioactive isotope refers to its half-life, which is the time required for half of the isotope's atoms in a sample to decay into a different element or isotope. During this period, the radioactivity decreases exponentially, meaning that after one half-life, 50% of the original isotope remains, and after two half-lives, 25% remains, and so on. This concept is crucial in fields like radiometric dating, nuclear medicine, and understanding radioactive decay processes.
Half of the original sample of a radio isotope remains after a half-life period. After two half-life periods, one-fourth of the radio isotope remains.
Not sure what you mean by "had-lives". After 3 half lives, approx 1/8 would remain.
An eighth remains.
12.5%
If I take a radioactive sample of 400 moles of an unknown substance and let it decay to the point of three half-lives I would have 50 moles left of the sample. 1/2 of what is left will decay in the next half-life. At the end of that half-life I will have 25 moles left of the unknown substance or 4/25.
Half-life is the time it takes for one half of the radioactive material to decay. It is logarithmic, so after two half-lives, one quarter remains - then one eighth - etc.
1/8 of the original amount remains.
Three half lives have elapsed. This can be determined by calculating how many times the original sample size must be halved to get to one eighth: (1/2) * (1/2) * (1/2) = 1/8.
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.
3 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.
1/8 = (1/2)3 which is in the form (1/2)n where n is the number of half lives undergone. Therefore the substance has passed three half lives
After 2 half lives, 25% of the original radioactive sample remains unchanged. This is because half of the sample decays in each half life, so after 1 half life, 50% has decayed, and after 2 half lives, another 50% has decayed, leaving 25% unchanged.