what is the half life of radioactive substance if 87.5% of any given amount of the substance disintegrate in 40 minutes

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Half-life of radioactive substance

Radioactive substances decay over time, which means that their nuclei disintegrate and emit radiation. The amount of time it takes for half of the atoms in a sample to decay is known as the half-life of that substance. The half-life is a characteristic property of each radioactive isotope and can be used to determine how long it will take for a sample to decay.

Calculating half-life

If 87.5% of a radioactive substance disintegrates in 40 minutes, we can use this information to calculate the half-life of the substance. We know that after one half-life, half of the remaining substance will have decayed. Since 87.5% of the substance has decayed, we can calculate how many half-lives have passed:

87.5% = 0.875

0.875 = (1/2)^n

n = log2(0.875) = 0.166

This means that 0.166 half-lives have passed. We can now use the formula for half-life to calculate the time it takes for one half-life:

t1/2 = t/n = 40 min / 0.166 = 240.96 min ≈ 241 min

Interpreting the result

The half-life of the radioactive substance is approximately 241 minutes. This means that every 241 minutes, half of the remaining substance will decay. After two half-lives (482 minutes), only one quarter of the original substance will remain, and after three half-lives (723 minutes), only one eighth will remain, and so on.

The half-life is an important property of radioactive substances, as it allows us to predict how long it will take for a sample to decay. This information is useful in a variety of applications, such as radiocarbon dating, nuclear medicine, and nuclear power generation.

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saya where u not get the ans

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ok

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k=2.303÷40loga÷a÷a-0.875=2.303÷40log8=0.0519per min.now t half =0.693÷0.0519=13.33min whose value =13 min20sec

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what for whom and why mansi and saya where u didn't got the ans

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it's ncert question

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how did u calculate this??

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Hmm

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the answer I didn't get it

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thank you

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13 min 20 sec

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