Radioactivity

Radioactivity
Radioactive (unstable) nuclei are generally
believed to be man made, however many
unstable isotopes are produced in large
quantities by “natural” occurring processes.
The decay always follows the same pattern described by radioactive decay law
Radioactive Decay Laws
dN
dt
N
dN
N
dt
N t N t e t
= ? ?
= ? ?
= ? ? ?
?
?
( ) ( ) ? 0
?: decay constant
N: number of radio-isotopes
N(t0)=N0: initial number of radio-isotopes
Half-Life of Radio-Isotope
N(t) = N ? e? ?t
0
? time (days) 131I (%)
0 100.0000
1 91.7411
2 84.1642
3 77.2132
4 70.8362
5 64.9859
6 59.6188
7 54.6949
8 50.1777
9 46.0335
10 42.2317
15 27.4446
20 17.8351
25 11.5903
30 7.5321
40 3.1809
50 1.3434
60 0.5673
70 0.2396
80 0.1012
90 0.0427
100 0.0180
Radioactive Clocks
dating isotopes
0
20
40
60
80
100
0 10000 20000 30000 40000
time [years]
activity [%]
226Ra
T 14C 1/2(14C)=5730 y
T1/2(226Ra)=1600 y
Example: If your 22920 year
old sample (4 half-lives) originally
had 1000 14C isotopes, how many
14C isotopes are left today?
[ ]
N y e
y y
N y
( [ ]) y
ln [ ] .
( [])
22920 1000 [ ]
2 5730 121 10
22920 62