00:01
Find a half life of a radioactive substance that decays at a continuous rate of 16 % per minute.
00:07
Okay, so we know that the equation which governs the radioactivity is given by a is equal to a0 times e raised 2 minus lambda t.
00:18
Now we are given that in every one minute when t is one, it decays 16%.
00:26
That decays at a continuous rate of 16 % it means that, that amount which is left, since it decays 16%, so the amount which is left at 100 minus 16, right, 100 minus 16 of a0, which is nothing but 84 percentage of a0, which is nothing but 0 .84a0, 0 .84 , all right.
00:50
So we know these things, so keeping these things in mind, we substitute it in the equation.
00:57
So we replace a by 0 .84 , a not.
01:00
A not, it remains a0.
01:02
Lambda remains lambda and t becomes one so a not is cancelled from both the sides and let's take natural log both sides so natural log of 0 .84 is natural log of e raise to minus lambda so this will become natural log of 0 .84 0 .84 this negative lambda comes down and natural this becomes natural log of e so this will become natural log of 0 .84 is negative lambda times natural log of e is just one.
01:30
So if we flip the equation and multiply negative one both sides, then lambda is negative of natural log of 0 .84.
01:38
And we know we are not supposed to find the lambda, which is the decay constant.
01:42
We are rather interested in finding the half life...