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# HALF LIFE

Half Life

Most of the students get confused in the numerical problems of physics or chemistry, even though they are not that much difficult but require a little attention and understanding. Half- life is one of the topics most students find hard to understand. The topic itself is simple but the numerical problems can create some confusion. This topic will help you to solve half-life problems with a simple method. So, first of all consider an example:-

Problem Statement:

An isotope of cesium-137 has a half-life of 30 years. Cesium-137 disintegrates over a period of 90 years. How much of cesium-137 would remain, provided the initial amount was 1g?

Procedure:
1. First, let us find out how many half-life 90 years are going to be. For that we will divide 90 with the half-life provide in the question.
2. T =90 years/30 years ,that will give us 3T ,that means 90 years will have 3 half-life.
3. As mentioned in the problem ,the initial amount of cesium is 1g
4. Now let’s find out how many grams of cesium will be left after 3 half-life
• Amount left after first half life (1T)  = 1/2 = 0.5 g
• Amount left after second half life (2T) = 0.5/2 = 0.25 g
• Amount left after third half life (3T) = 0.25/2 = 0.125 g
So, the amount of cesium left after 3T will be 0.125.

The next step, what if they ask the percentage of the cesium left?
This is actually simpler, we already found out that there are 3 half-life.
We will start from a 100%

• After 1T=100/2 =50%
• After 2T=50/2= 25%
• After 3T =25/2=12.5%
So, after 3 half-lives the percentage of cesium left will be 12.5%!

The third step, what if you were asked to find out the fraction of what is left after the 90 years?
Here is how you do it:
(Keeping in mind 3 half –lives)
After 1 half-life, we will lose 1/2 of the initial amount.
After 2 half –life, we will lose another half i.e. 1/2 of 1/2
After 3 half-life, another half will be gone i.e 1/2 of (1/2 of 1/2)

This can be written as:
1/2 *1/2*1/2 =1/8
There we have it ,1/8 is the answer.
If   we divide 1g by 8 we will get 0.125g, sounds familiar? Of course it does.
If you find this easy to understand, we can move on to the next level :)

Entry # 6
By Javeria Saeed

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