Find the activity of 1mg of radon 222 whose half life is 3.825 days
Answers
Answer:
Explanation:Why use a term like half-life rather than lifetime? The answer can be found by examining Figure 1, which shows how the number of radioactive nuclei in a sample decreases with time. The time in which half of the original number of nuclei decay is defined as the half-life, t1/2. Half of the remaining nuclei decay in the next half-life. Further, half of that amount decays in the following half-life. Therefore, the number of radioactive nuclei decreases from N to
N
2
in one half-life, then to
N
4
in the next, and to
N
8
in the next, and so on. If N is a large number, then many half-lives (not just two) pass before all of the nuclei decay. Nuclear decay is an example of a purely statistical process. A more precise definition of half-life is that each nucleus has a 50% chance of living for a time equal to one half-life t1/2. Thus, if N is reasonably large, half of the original nuclei decay in a time of one half-life. If an individual nucleus makes it through that time, it still has a 50% chance of surviving through another half-life. Even if it happens to make it through hundreds of half-lives, it still has a 50% chance of surviving through one more. The probability of decay is the same no matter when you start counting. This is like random coin flipping. The chance of heads is 50%, no matter what has happened before.
The figure shows a radioactive decay graph of number of nuclides in thousands versus time in multiples of half-life. The number of radioactive nuclei decreases exponentially and finally approaches zero after about ten half-lives.
Figure 1. Radioactive decay reduces the number of radioactive nuclei over time. In one half-life t1/2, the number decreases to half of its original value. Half of what remains decay in the next half-life, and half of those in the next, and so on. This is an exponential decay, as seen in the graph of the number of nuclei present as a function of time.
There is a tremendous range in the half-lives of various nuclides, from as short as 10−23 s for the most unstable, to more than 1016 y for the least unstable, or about 46 orders of magnitude. Nuclides with the shortest half-lives are those for which the nuclear forces are least attractive, an indication of the extent to which the nuclear force can depend on the particular combination of neutrons and protons. The concept of half-life is applicable to other subatomic particles, as will be discussed in Particle Physics. It is also applicable to the decay of excited states in atoms and nuclei. The following equation gives the quantitative relationship between the original number of nuclei present at time zero (N0) and the number (N) at a later time t: N = N0e−λt, where e=2.71828… is the base of the natural logarithm, and λ is the decay constant for the nuclide. The shorter the half-life, the larger is the value of λ, and the faster the exponential e−λt decreases with time. The relationship between the decay constant λ and the half-life t1/2 is
λ
=
ln
(
2
)
t
1
/
2
≈
0.693
t
1
/
2
.
To see how the number of nuclei declines to half its original value in one half-life, let t = t1/2 in the exponential in the equation N = N0e−λt. This gives N = N0e−λt = N0e−0.693 = 0.500N0. For integral numbers of half-lives, you can just divide the original number by 2 over and over again, rather than using the exponential relationship. For example, if ten half-lives have passed, we divide N by 2 ten times. This reduces it to
N
1024
. For an arbitrary time, not just a multiple of the half-life, the exponential relationship must be used.