DECK 6 — COUNTING STATISTICS & DISTANCE LAW

What statistical distribution describes radiation counting events?

The Poisson distribution describes radiation counting events.

Why does radiation follow a Poisson distribution?

Counts occur randomly and independently with constant average rate.

What is the mean of a Poisson distribution?

The mean of a Poisson distribution is equal to the expected number of counts.

What is the variance of a Poisson distribution?

The variance of a Poisson distribution is equal to the mean.

What is the standard deviation for Poisson counting?

The standard deviation is the square root of the mean number of counts.

Why does standard deviation increase with count number?

Statistical fluctuations grow with the square root of the counts.

Why does relative uncertainty decrease with more counts?

Relative uncertainty equals 1 divided by the square root of the counts.

What is the relative standard deviation for N counts?

Relative deviation equals 1/√N.

What is the uncertainty in count rate R = N/t?

The uncertainty is σR = √N / t.

Why is longer counting time used in low-count measurements?

Longer time increases N and reduces statistical uncertainty.

What approximation applies when counts are high?

The Poisson distribution approaches a Gaussian distribution for large N.

What is the standard deviation of a Gaussian distribution from counting?

The Gaussian standard deviation equals √N for large N.

What is propagation of error?

Propagation of error is combining uncertainties when calculating derived quantities.

What is the uncertainty of a sum or difference A ± B?

The uncertainty is √(σA² + σB²).

What is the uncertainty of a product or quotient A·B or A/B?

The relative uncertainty is √((σA/A)² + (σB/B)²).

What is the purpose of background subtraction?

Background subtraction isolates the true count rate of the radiation source.

What is the uncertainty of net counts Nnet = Ntotal − Nbkg?

The uncertainty is √(Ntotal + Nbkg).

Why is background always measured in counting experiments?

Background contributes to the total counts and must be removed for accurate results.

What does the inverse square law describe?

The inverse square law describes how radiation intensity decreases with the square of the distance from a point source.

Why does radiation follow the inverse square law?

Photons spread over a larger spherical area as distance increases.

What is the mathematical form of the inverse square law?

I ∝ 1 / r² for a point source in free space.

How do you test the inverse square law in the lab?

Measure count rate at different distances and check whether R·r² is constant.

Why may the inverse square law fail at small distances?

Detector size, source size, and scattering distort the point-source approximation.

What is the effect of dead time on counting experiments?

Dead time reduces observed count rate and distorts high-rate measurements.

Why is dead time correction sometimes required?

High count rates cause event losses that must be corrected for accurate results.

What model describes most radiation counters for dead time?

Most counters follow the non-paralyzable dead-time model.

What is the non-paralyzable dead-time correction equation?

Rtrue = Robs / (1 − Robs·τ).

Why must count rate be kept low for accurate statistics?

High rates cause pile-up, dead-time losses, and distorted distributions.

Why is statistical uncertainty fundamental in radiation detection?

Radioactive decay is inherently random, producing unavoidable fluctuations.

Why are replicate measurements useful in counting experiments?

Replicate measurements reduce random error and verify statistical behavior.

What determines whether Poisson or Gaussian statistics should be used?

Use Poisson for low counts and Gaussian when counts exceed approximately 30.