00:01
Hello, welcome to this lesson.
00:03
In this lesson, we have 100 gram sample of isotopes sodium that decays to 30 grams after 26 hours.
00:11
So the first part will find the half life.
00:16
Before we do that, we should be able to look for the decay constant.
00:23
Here we have this essential formula where n is called 2 and 0e to the 0 .e to the negative kt, where n is the substantive.
00:31
Amount of substance left at any given time t and then notice the original substance that original mass that was there here we have 100 grams the case that decay constant so given the initial condition given to us where we had after 26 hours we had 30 grams that was left left.
01:10
So after time t, there was n substance that was left.
01:16
All right.
01:17
So here, now we have the n as 30.
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The n of 100, the original substance that we had.
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And e to the par negative k.
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Now the t is the time.
01:40
So this was done after 26 hours.
01:44
All right.
01:45
So with this we have 30.
01:47
That is equals to 100 100 each the power negative 26k so what we do is that we take the lane of both sides the natural look are in both sides then we have the lane 100 each the power negative 26k okay so land 30 and this is equal to land 100 okay so this defunction.
03:09
That's actually two ways of doing this.
03:11
The first method is this.
03:14
The second we could have divided both sides by 100.
03:17
So that we have 0 .3 that is called to e to the power negative 26.
03:23
Okay.
03:24
All right.
03:25
Then we take it from there.
03:28
Right.
03:29
Just so, so another good way of getting it done.
03:34
Okay.
03:34
So here we have lenn.
03:39
30 minus lane 100 this is equals to negative 26k where the lane and the lane and the e will go away.
03:53
All right.
03:57
So at the end of the day, we have lane 30 minus.
04:09
Okay, so with this, we can divide both sides by negative 26.
04:15
So that here we have k which is equals to 0 .04631.
04:37
Alright.
04:40
So now essentially we can write and that is equals to nought, then e to the power, negative.
04:49
Instead of k, we will put 0 .04 631, then t...