Radioactive Decay as a Probability Distribution

N

0

1500

n

1

radioactive constant λ

0.001

filling

axis

none

General

:Exp[-1630.7] is too small to represent as a normalized machine number; precision may be lost.

Radioactive decay is often described in terms of a probability distribution, since one cannot predict when an individual atom will decay. The probability that

n

particles will disintegrate in the time interval

Δt

is given by

ω=

1

π

-3/2

(2

N

0

λΔt)

exp-

2

(n-

N

0

λΔt)

],

where

N

0

is the initial number of nuclei present and

λ

is the decay constant characteristic of the radioactive isotope.