00:01
In this problem, we are given that at time t equals to 0, 10 micromoles of an isotope are present.
00:14
And further we are given that this isotope has a half life of 14 days.
00:24
We are asked to find out how much of the isotope remains.
00:40
After 11 days.
00:45
So here since we have a decay model we can use a equals to a not times e raised to the part negative lambda t where a denotes the amount of the isotope and lambda denotes the decay rate.
01:01
So here since we are given initially 10 micromoles are present it implies that the value of a not equals to 10.
01:10
So this can be be written as a equals to 10 times e raised to the power negative lambda t.
01:17
Next, in order to find out the value of lambda, we make use of the condition that the half life is 14 days.
01:24
That is, a of 14 equals to 10 divided by 2, which is 5 micromoles.
01:32
So making use of this, we get 5 equals to 10 times e raise to the power negative 14 lambda.
01:42
So now dividing by 10 on both sides, we get 1 over 2 equals to e raised the part negative 14 lambda.
01:52
So in order to find out the value of lambda, we take natural log on both sides.
01:56
So we get natural log of 1 over 2 equals to negative 14 times lambda...