00:01
To determine the mass that is left after 50 years with a half -life of 20 years, we first need to calculate the decay constant, or i guess they call it the disintegration constant.
00:14
It's also known as just simply the rate constant.
00:18
To do this, we'll use the half -life equation, where k is equal to the natural log of 2 divided by the half -life.
00:25
The half -life in this case is 20 years.
00:28
So we get 0 .0 .3465 or 347, 1 over years.
00:40
Then we can use the first order integrated rate log, which is what radioactive samples follow, and that is the natural log of the amount at time t is going to be equal to negative k multiplied by the time that has elapsed, plus the natural log of the amount at times zero.
01:00
So negative k is negative 0 .347, 0347, 1 over years.
01:12
And the time that we want to consider is 50 years, and then plus the natural log of the amount at time 0, which is 400 grams.
01:24
Grams is abbreviated just g.
01:26
And so we get the natural log of the mass at time t being equal to 4 .258 or 56 sorry yeah 2.
01:47
I'm sorry 4 .258 or 4 .26 we then take the anti -natural log of both sides that is e to the and we get 70 .7 grams remaining.
02:03
So for the next question, we just need to calculate the disintegration constant for nickel with a half -life of 5 .2 years...