Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
Radioactive decay work so each atom has a low probability of decaying at each moment in time. They have also no memory so the probability does not change over time.
Let’s say we have 1000 million atoms and 5% decay in each time unit, that means 95% survive. So after 1-time unit we have 1000* 0.95 = 950 million after two time units we have 1000* 0.95 * 0.95 = 1000 * 0.95 ^(2) = 902.5 million
Lets do that. The number is rounder than do integer million but calculations are done with decimals. The number are at the end of the post
We have 500 between 13-14 time units we have 250 at 27= 13.5 * 2 we have 125 after 40-41 time units 13.5 * 3 = 40.5
So the number of atoms we have get halved after around 13.5 time tune if we use 5% each time unit. You always get a result like this is if you in each unit of time use come a percentage of all. You could do the calculation 0.95 ^ t = 1/2 and the solution is t is aproximalty 13.5134
This only works if you have a huger number of atoms, there is a reason I used millions. If you only have a single atom you have no idea when it will decay but if you have a billions you can be quite sure how many will decay in a unit of time. A single atom can in principle last forever and never decay even if it is radioactive. It is not likely but possible.
So half-life is the average time it takes for half of a large sample of atoms to decay. There is not a full life for an atome.
It is a bit like if you have a single six-sided dice each throw can be 1 to 6 but if you have 100 dice and throw all of them and take the average value it will be close to 3.5.
0 1000
1 950
2 903
3 857
4 815
5 774
6 735
7 698
8 663
9 630
10 599
11 569
12 540
13 513
14 488
15 463
16 440
17 418
18 397
19 377
20 358
21 341
22 324
23 307
24 292
25 277
26 264
27 250
28 238
29 226
30 215
31 204
32 194
33 184
34 175
35 166
36 158
37 150
38 142
39 135
40 129
41 122
42 116
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