Inverse Square Law (γ radiation)
Research project on the inverse square law. I was confused on how the geiger tube's exposed area was taken into account.
Net count rate vs distance
model curve + your measurements
Graph of y=1/x2. Shoutout to all the mathematicians you the real physicists
Real-world examples
Torch brightness (lux meter)
D0 = 1200. r0 = 0.5. Anyone else notice a pattern with things emitted from a point?
r = 0.50 m
1200 lx
Radiation dose rate (γ)
Dose rate drops with distance. Figures used: D0 = 18. r0 = 0.5
r = 0.50 m
18.00 µSv/h
Wi-Fi / radio signal (relative)
Power per area spreads out. D0 = 100. r0 = 0.5. Things spread out inverse square-ly. They should make a law about this...
r = 0.50 m
100%
(r₀/r)² is the scale factor vs the reference distance r₀ — e.g. 0.06 means the reading is 6% of what it was at r₀. These equations are made by me. They follow: D(r)=D0(r0/r)² where D(r) is the dose rate for radius r, r0 is the example distance and r is the new distance you decide. This is to make the law clearer.
Research notes
The process:
After struggling to understand how the equation accounts for only a portion of the counts being received, I turned to modelling the equations for answers. Assume you have a point source, like the one shown in the model. It emits particles uniformly in all directions (unbelievable at first). Since it is the centre of its own sphere, the distance between it and the point source will be its radius. If the source emits S particles per second, the particles per second per square metre is given by S/4πr2. But the detector doesn't measure all of this, just a small area. Let the area of the detector facing the source (m2) be x. Detection efficiency was ignored. The counts per second due to source is then equal to the particles per second per square metre multiplied by the area of the detector facing the source. Hence: xΦ(r) = xS/4πr2. This gives net count rate = K/r2. I wanted to account for background radiation so I allowed users to choose an amount and then modelled it using Cnet = Cgross - Cbg. Note that the 3D model does not do any of this math, all it is linked to is the radius slider. In practice, the mathematics behind this are more precise as they utilise a Poisson distribution linked to a normal approximation (for large lambdas) and knuths algorithm (for small lambdas) which I found on github and copied and pasted into my code. The count time was included in this distribution so I added a slider for it, improving accuracy of results in order to counteract point source randomness.
Controls
Distance r (m)
Inverse-square constant K (s⁻¹·m²)
Background Counts (s⁻¹)
Count time T (s)
Model results
Counts from source (Counts per second)
12.50 s⁻¹
Background (Counts per second)
6.00 s⁻¹
Total geiger reading (source + bg counts)
18.50 s⁻¹
Last N (counts)
—
Last C = N/T
—
Last Counts from source = Total - background
—
Model
Cnet = K / r²
Measurement
N counts in time T
C = N/T
Counts from source = Total counts - background counts
Your data
No points yet. Take a measurement.