A gamma beam crossing shielding thins out exponentially, I = I0e-μx. Set the photon energy, pick a material and drag the thickness, and the simulator reports the transmitted percentage, the attenuation coefficient μ and the half-value layer as you go.
Gamma Ray Shielding
A collimated gamma beam crosses a slab of shielding and thins out as I = I0e-μx. Change the energy, the material and the thickness, and watch how much gets through. The beam never reaches zero.
Narrow-beam values interpolated from NIST mass attenuation tables.
What Is the Gamma Ray Simulator?
The gamma ray simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Set photon energy, shield material and thickness, and watch transmitted intensity follow I = I0 exp(-mu x) live. It reports transmitted i / as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Photon energy in mega electronvolts | 0.1 – 2 MeV | 0.001 |
| Shield thickness | 0 – 20 cm | 0.1 |
How to Read the Beam as It Crosses the Slab
The picture is deliberately literal. A collimated beam enters from the left at full strength, and its width and brightness fall away as it works through the slab. What emerges on the right keeps travelling at whatever strength it has left, because nothing further is there to absorb it. The pale tick marks ruled across the slab are spaced one half-value layer apart, so you can count them off and know the beam has halved at each one.
Start with the photon energy slider, because it behaves backwards from most expectations. Push it from 0.1 MeV up towards 2 MeV and the attenuation coefficient μ falls: the half-value layer stretches, the tick marks spread apart, and more of the beam survives the same slab. Higher-energy gamma rays are harder to stop, not easier. The two source presets make the point in one click, since a Co-60 photon at 1.25 MeV punches through noticeably more lead than a Cs-137 photon at 0.662 MeV. If you want the energy of an individual photon from its frequency or wavelength, the photon energy calculator handles that side of the arithmetic.
Now drag thickness. The transmitted reading falls fast and then keeps falling, but it never lands on zero, and that is the single most important thing this simulator has to teach. Shielding is not a threshold you cross. Each additional centimetre removes the same fraction of whatever is still there, so the numbers march down through one per cent, then a thousandth of a per cent, without ever arriving at nothing. Ten half-value layers still leave about one photon in a thousand. Engineers do not design shielding to stop gamma rays; they design it to reduce them to a dose they are willing to accept.
Switching material at a fixed thickness shows why lead earns its reputation. Twenty centimetres of water barely dents a 1.25 MeV beam, while a couple of centimetres of lead does far more, because μ is the mass attenuation coefficient multiplied by density and lead brings both a high atomic number and 11.35 g/cm3. One honest caveat: this is narrow-beam geometry, so scattered photons are treated as gone. Real rooms need a build-up factor and more thickness. For how the source itself weakens over time rather than over distance, see the guide to half-life, and for the full picture of where gamma rays come from and what they are used for, read gamma rays: properties and uses.
Frequently asked questions
Why doesn't the transmitted intensity ever reach zero?
Because attenuation is exponential, not subtractive. Each centimetre of shielding removes the same fraction of whatever is left, so the beam is halved, then halved again, and never quite arrives at nothing. Doubling the thickness squares the transmitted fraction rather than cancelling it. In practice you shield until what gets through is acceptably small, not until it is zero, because zero is not on the table.
What is a half-value layer?
The half-value layer, or HVL, is the thickness of a given material that cuts the beam to 50 per cent. It is ln(2) divided by the linear attenuation coefficient, so it depends on both the material and the photon energy. It is useful because it turns an exponential into simple counting: two HVLs leave a quarter, three leave an eighth, ten leave about one part in a thousand. The tick marks drawn on the slab are spaced one HVL apart.
Why does more energy mean more penetration?
Over the range this simulator covers, from 0.1 to 2 MeV, the dominant interaction is Compton scattering, and its cross-section falls as photon energy rises. Less interaction means a smaller attenuation coefficient, a larger half-value layer, and more of the beam getting through. This is why the energy slider works the opposite way round to most people's expectation: a harder source needs thicker shielding, not thinner.
Does this simulator include scatter build-up?
No. It models narrow-beam, well-collimated geometry, where any photon that scatters is treated as removed from the beam. Real shielding in a real room also receives photons that scattered off walls and arrived from odd angles, which is handled with a build-up factor greater than one. That means genuine shielding thickness is larger than the narrow-beam figure shown here, so treat these numbers as a floor rather than a design value.
Which materials are included?
Lead, water, ordinary concrete and aluminium. Each carries its own density and its own table of mass attenuation coefficients taken from NIST, and the simulator interpolates between the tabulated energies on a log-log scale rather than extrapolating past the ends. Comparing lead against water at the same thickness shows why dense, high atomic number materials are the standard choice for gamma shielding.
References & formula source
- J. H. Hubbell & S. M. Seltzer - NIST X-Ray Mass Attenuation Coefficients, Tables 3 and 4 (lead, aluminium, water, ordinary concrete).
- Krane - Introductory Nuclear Physics, Chapter 7, interaction of gamma radiation with matter.
- Knoll - Radiation Detection and Measurement, Chapter 2, attenuation and narrow-beam versus broad-beam geometry.