So, I was told that, while radioactive elements have half lives that have been estimated (i.e. the time it takes for a material to decay to half it’s mass), kt’s not entirely predictable how often particles will decay in a given moment. If all that is true (which it might not be, feel free to correct in replies), is there a chance, if microscopically small, that a uranium rod could just fizzle out of existence in a matter of nanoseconds?
In: 6
Yes every atom could decay in the next moment of time, it is just extremely unlikely.
A half-life is a mathematical result of atoms that in each moment of time have a small chance of decaying and the process has no memory.
So if you have atoms has a 1% probability of decaying each minute and a lot of them the result will be that there is a period of time that half decay. Because there is no memory the remaining will take the same time to half again.
You can calculate the half-life by install looking at the surficial change of 99%
You now need to solve the equation 0.99^n = 1/2 and the answer is n is approximately 69 seconds.
You can calculate the probability all decay the first second too. Lets just use 100 atom the answer is then 0.01^100 = 10^-200
That number is 0.0 and another 198 zero before a 1.
That is number so large even if you had all the atoms in the universe available for each second since the start of the universe you are nowhere close to likely observing what happen with 100 atoms
In reality, 100 atoms is extremely few. 1 gram of matter is in the order of a billion billion billion atoms. The half-life of the uranium isotope we find in nature is hundreds of million or billion of years.
The result is for U-238 you lily have 12445 atoms that decay per second and a gram. You have around 2 thousand billion billion atoms in 1 gram of U-238
Latest Answers