# A Model for Successive Radioactive Decays

A Model for Successive Radioactive Decays

Radioactive decay is a statistical process that depends on the instability of the particular radioisotope.

For two successive decay processes, total activity (or number of disintegrations per second) is given by the green curve for :

dN/dt

dN/dt=-(exp[-t)+/(-)(exp[-t]-exp[-t]))

λ

1

N

0

λ

1

λ

2

λ

2

λ

1

λ

1

λ

2

where and are the decay constants for the two radioactive components (unstable nuclei or isotopes) and is the total number of nuclei at time . For example, if the first component is Bi, with a half-life of 19.7 minutes and the second component is Pb, with a half-life of 26 minutes, the decay constants are =5.86× and =4.44×, respectively.

λ

1

λ

2

N

0

t=0

214

214

λ

1

-4

10

λ

2

-4

10

In this Demonstration we use the relative values of radioactive constants with the "range without intersection".

The blue curve represents the second (or daughter) isotope :

N

2

N

2

λ

1

N

0

λ

1

λ

2

λ

2

λ

1