00:01
For this problem on the topic of nuclear physics, we are told that strontium -90 has a half -life of 29 years, and if a one -meageton bomb produces 400 grams of strontium -90 and the fallout spreads uniformly over 2 ,000 kilometers square of an area, we want to know the ground area that would hold an amount of radioactivity that is equal to the allowed limit for a single person, this limit being 74 ,000 counts per second.
00:27
Now, the count rate in the area in question is given by our.
00:31
Which is equal to lambda times n, where lambda is the decay constant and in the number of radioactive nuclei.
00:37
Since these spreading is assumed uniform, the count rate 74 ,000 is given by r is equal to lambda times n, which is lambda times big m over little m times little a over big a, where big m is the mass of strontium -90 produced little a, the mass of a single strontium -90 produced little a the mass of a single strontium 90 nucleus, big a, the area over which the fallout occurs, and little a, the area in question.
01:08
Now we know that lambda is equal to the natural log of 2 divided by the half -life for strontium -90, and so solving the equation above for little a, we get this to be big a into little m over big m times r over lambda...