00:01
Hi there, so for this problem we have a radioactive sample that contains 239 plutonium and with an activity that is given and that activity is two times 10 to the 17, okay.
00:21
And this in units of bed carols given that the half -life for this element is 4 .96 and this is in hours, okay.
00:38
So the question is, what is the mass of plutonium in the sample? so we determine that mass.
00:44
Now, the first thing that we are going to do is to transform the half -life that is given in hours to seconds, okay.
00:51
Because remember that bed carols is just one divided by seconds, right.
00:58
So once we have this, we just need to, well, let's do the transformation here.
01:04
First, we're going to pass this into minutes because we know that one hour equals to 60 minutes.
01:11
And then we know that one minute equals to 60 seconds.
01:18
So then by doing this product in here, let me calculate this quickly to obtain this in seconds.
01:29
So that will be 4 .96 times 3 ,600.
01:34
This will give us in seconds, 17 ,856.
01:42
Okay, this is in seconds, right.
01:44
So to obtain this, we use the following formula.
01:50
We know that the activity is just lambda where lambda is the decay constant that we need to determine.
01:56
This times the apogradus number, we're gonna label just simply as n.
02:00
Then this times the mass and then this divided by the atomic mass.
02:07
Well, let's put that as capital m, okay.
02:13
The atomic mass.
02:13
For this case, the atomic mass, because it is 239 plutonium, then the mass for this is going to be 239 grams per molt.
02:28
Now, the decay constant, we can obtain it by the napierian logarithm of two divided by the half -life that we are given...