00:01
First, we'll recognize that the rate of decomposition will be equal to the decay constant multiplied by the number of radioactive nuclides.
00:12
So knowing this, we can rearrange the equation to solve for k, which is apparently what you did because you got the same answer as i did.
00:21
The rate is 3 .7 times 10 to the 10 decays per second, and the number of radioactive nucleides will be the 1 gram divided by the molar mass of the radium 226.
00:43
Then when we know moles of radium 226, we'll multiply by avagadro's number to get n, which will be the number of radioactive nuclides.
00:52
And we get 1 .39 times 10 to the negative 11, 1 over seconds.
00:57
Half -life can then be calculated from the decay constant by dividing it into the natural log of 2.
01:02
And i get the same.
01:03
Same thing you got, 4 .99 times 10 to the 10 seconds.
01:08
So now to determine the activity after 300 years, we'll use the first order integrated rate law as all decays follow first order kinetics, where the natural log of the activity at time t will be equal to negative k, the k we just determined, multiplied by the time, the time they've given us is in years, but the decay constant is in one.
01:34
Over seconds, so we need to convert the years into seconds.
01:40
To do that, an average year is 365 .25 days due to leap year.
01:49
One day is 24 hours, and one hour is 3 ,600 seconds...