Physics 490 – Project Lab Lab B2: Radioactive Decay, Counting Statistics, and the Geiger Tube Jack Young Richard Breazeale Ryan Phelan

Counting Statistics - Topics Read and interpret the Chart of the Nuclides. Observe the difference between α, β, and γ decays. Observe the properties of the Gaussian and Poisson distributions.

Chart of Nuclides

α, β, and γ Decays α decay β decay γdecay γ decay

Measuring Decays The Geiger-Muller tube and associated equipment

Science Workshop

Science Workshop Settings

Excel – Statistical Analysis

Science Workshop

Science Workshop - Model

Science Workshop - Spreadsheet

Science Workshop - Parameters

Science Workshop - Plot

Science Workshop – Curve Fit

The Poisson Distribution  The Poisson distribution can be obtained from the binomial distribution if we let the number of events n go to infinity, where the most probable number of successes x remains constant so that p goes to zero.

Binomial Theorem The Poisson distribution describes the large-n limit (k large or small). We define the average number of events as x and the average number of events per measurement p so that x = np. If n is large compared to k and p is very small compared to 1, we can approximate as follows: Poisson Ditribution

The Poisson distribution is applied generally to situations where only a few events are counted. It is equally valid when large numbers of events are counted, but the Gaussian distribution can be used then, and it is easier to use. Substituting x for np, the Poisson distribution becomes:

Poisson Distribution Poisson distributions with different mean values.

The End