A Model for Successive Radioactive Decays

N

0

9

radioactive constant

λ

1

radioactive constant

λ

2

filling

axis

none

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=-

λ

1

N

0

(exp[-

λ

1

t)+

λ

2

/(

λ

2

-

λ

1

)(exp[-

λ

1

t]-exp[-

λ

2

t]))

,

where

λ

1

and

λ

2

are the decay constants for the two radioactive components (unstable nuclei or isotopes) and

N

0

is the total number of nuclei at time

t=0

. For example, if the first component is

214

Bi

, with a half-life of 19.7 minutes and the second component is

214

Pb

, with a half-life of 26 minutes, the decay constants are

λ

1

=5.86×

-4

10

and

λ

2

=4.44×

-4

10

, respectively.

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

(exp[-

λ

1

t]-exp[-

λ

2

t])/(

λ

2

-

λ

1

)

.