T ½ The fun applied math part And you. Recall The decay curve of a radioactive decay process is exponential. That makes it much more difficult to determine.

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Presentation transcript:

t ½ The fun applied math part And you

Recall The decay curve of a radioactive decay process is exponential. That makes it much more difficult to determine how much of an initial sample will remain after a given time interval (unless you graph out the entire decay process) But we can calculate what we are looking for using applied math --- YES!!!!!!!!!!

Let me provide you with an example I start with 1.0g. of 3 1 H t ½ = 12.3 years ??? How many grams of 3 1 H will remain after 24.6 years???

How should I approach this problem? 1) Calculate the ratio of time elapsed to the t ½ interval. We will call this ratio “n” t = 24.6 = 2 = n t ½ 12.3

Then what??? 2) Plug into this equation to calculate the percentage of the original sample left: (1/2) n (1/2) 2 =.25 so 25% of the original sample remains 3) Multiply by the original grammage 1.0 g (.25) =.25 grams remain (from the original 1.0 g sample)

Hey – you try a few now!!! Np has a ½ life of 2.0 days If you start with a 4.0 g sample, how many grams will you have after 8 days??? Step 1: n = t/t ½ = 8/2 = 4 Step 2: ( ½ ) n = ( ½ ) 4 =.0625 (or 6.25%) Step 3: (4.0 g)(.0625) = 0.25g left

I think you get the idea – just a few more then 1) 194 Po has a t ½ of 0.7 seconds. How many grams of a 3 kg sample remain after 2 minutes Answer: 1 x g. 2) 210 Po has a t ½ of 138 days. How much of a 2.2 kg sample remains after 1.5 minutes? Answer: 2.199kg (2199 g)

NOW That was fun!!!!!!!!!