# Probabilistic description of radioactivity based on the good-as-new postulate

## Abstract

The good-as-new postulate applied to radioactivity says: the conditional probability that a radioactive atom will live past time s + t, given that it has lived past time s, is equal to the unconditional probability that it would have lived past time t, starting from time zero. This postulate leads directly to the conclusion that the decay time of a radioactive atom is an exponentially distributed random variable. Add the postulate that the decay times of individual atoms in an aggregate of identical radioactive atoms are independent, and a complete description of the random behavior of an aggregate can be constructed. This approach stresses from the outset the randomness inherent in the radioactive decay process, and is offered as a complement to the deterministic approach that treats fluctuations about mean values. All results are exact within the context of the model and are applicable to aggregates of any size - no assumptions about large numbers are required. 1 figure, 1 table.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of California, Livermore

- OSTI Identifier:
- 5754135

- Resource Type:
- Journal Article

- Journal Name:
- Am. J. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 47:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; RADIOACTIVITY; MATHEMATICAL MODELS; MONTE CARLO METHOD; RANDOMNESS; STOCHASTIC PROCESSES; 653005* - Nuclear Theory- Radioactive Decay

### Citation Formats

```
Barnett, C.S.
```*Probabilistic description of radioactivity based on the good-as-new postulate*. United States: N. p., 1979.
Web. doi:10.1119/1.11892.

```
Barnett, C.S.
```*Probabilistic description of radioactivity based on the good-as-new postulate*. United States. doi:10.1119/1.11892.

```
Barnett, C.S. Thu .
"Probabilistic description of radioactivity based on the good-as-new postulate". United States. doi:10.1119/1.11892.
```

```
@article{osti_5754135,
```

title = {Probabilistic description of radioactivity based on the good-as-new postulate},

author = {Barnett, C.S.},

abstractNote = {The good-as-new postulate applied to radioactivity says: the conditional probability that a radioactive atom will live past time s + t, given that it has lived past time s, is equal to the unconditional probability that it would have lived past time t, starting from time zero. This postulate leads directly to the conclusion that the decay time of a radioactive atom is an exponentially distributed random variable. Add the postulate that the decay times of individual atoms in an aggregate of identical radioactive atoms are independent, and a complete description of the random behavior of an aggregate can be constructed. This approach stresses from the outset the randomness inherent in the radioactive decay process, and is offered as a complement to the deterministic approach that treats fluctuations about mean values. All results are exact within the context of the model and are applicable to aggregates of any size - no assumptions about large numbers are required. 1 figure, 1 table.},

doi = {10.1119/1.11892},

journal = {Am. J. Phys.; (United States)},

number = ,

volume = 47:2,

place = {United States},

year = {1979},

month = {2}

}