# Half Life of radioactive element

1. Jul 22, 2010

### abrowaqas

It takes an infinite time for complete decay of a radioactive element. but on the same time we calculate the half life of radioactive material i-e T-1/2 = ln 2 / lamda. is that means that if we double the half life time we could reach the total life time of radioactive decay so on contrary we have reached the infinity. which is impossible. how can this be cleared.

2. Jul 22, 2010

### mathman

Your statement is a little confusing. After one half-life, half the original material remains. After another half-life, one-quarter (half of half) remains. After another half-life, one-eighth remains, etc.

3. Jul 23, 2010

### abrowaqas

i said that if we double the half life that is we multiple the half life by two so we will get the full life of radioactive element.... but how is this possible coz full life of radioactive element is at infinity... so whats the confusion here.

4. Jul 23, 2010

Wrong,if you double the half life what you get is just that,double the half life or two half lives.It is misleading to talk about "full life" of a radioactive substance because one of the assumptions made in the mathematical treatment of half life becomes less valid as the number of radioactive atoms gets smaller.

5. Jul 24, 2010

### statphys

I doesn't take infinity for the last bit of a quantity of a radioactive substance to decay. The process is a statistical one applicable to large numbers of particles and won't hold when you are right down there at small numbers. I think you are taking the mathematical formalism of radioactive decay a little too literally.

6. Aug 4, 2010

### Jesvant

no youre wrong, half-life decay is like a log function, so doubling the time wont mean it would decay

7. Aug 8, 2010

### Xray

I believe that you are confusing radioactive decay with the mathematical function known as an infinite series. It is true that if you continue to divide any number by 2, you will never reach zero, although you will get infinitely close to it. But when you are dealing with a descrete number of items, such as atoms in a chunk of radioactive material, eventually you will get down to a very small number, say 8, then 4, then 2, then 1, then zero! Therefore, it is NOT an infinite series.