use the half-life information to complete each table. (The formula 𝒩=𝒩0 e^k t is not required.)

Use the half-life information to complete each table. (The...

use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.)
(a) Uranium- 228: half-life $=550$ sec
(b) Uranium-238: half-life $=4.9 \times 10^{9}$ years

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Key Concepts

Half-Life

Half-life is the period of time required for half of a given amount of a radioactive substance to decay. This concept is crucial for understanding the rate of decay and for calculating the remaining quantity of a substance after a certain period, regardless of whether an explicit exponential decay formula is used.

Radioactive Decay

Radioactive decay is the process by which unstable nuclei lose energy by emitting particles or radiation. It is a natural and spontaneous phenomenon that explains the transformation of elements such as uranium into different elements over time.

Transcript

00:03 So we're given that the half -life for a certain isotope is 550 seconds and that the initial amount was 8 grams.

00:11 After 550 seconds elapsed, how much is left? well, this is a half -life, so the amount left is going to be half of what we started with, which is 8 times 1 -half, which will be 4 grams.

00:27 Then after another half -life, how long will it have been? well, 550 plus 550 equals 1 ,100.

00:37 So if another half -life has elapsed, our four grams is going to be reduced by half again.

00:46 So four times a half is two grams.

00:52 And then another half -life later, our total time will be 1 ,6 ,500.

00:59 50 seconds and our two grams will be reduced in half, which is so two times a half equals one gram.

01:12 And then after another 550 seconds or another half life, the total time elapsed will be 2200 seconds.

01:22 And that one gram will be reduced in half.

01:27 And so we'll get one times one half equals 0 .5 grams.

01:39 We're given another isotope that has a half life of 4 .9 times 10 to the ninth years.

01:46 And we started with 10 grams.

01:49 So when the amount left is five grams, that's half.

01:56 Right? so 10 times a half equals five grams.

02:01 So that means a half life has elapsed.

02:04 So that means we'd have 4 .9 times 10 to the 9th years...

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