Radiation Shielding Attenuation
Compute the radiation intensity after passing through shielding, I = I₀·e^(−μ·x), by the exponential attenuation law, from the initial intensity (I₀), the material's linear attenuation coefficient (μ) and the thickness (x). Unlike alpha and beta particles (which have a finite range), gamma rays and X-rays are only exponentially attenuated — never fully blocked. It is the basis of shielding calculation. Enter the initial intensity, the attenuation coefficient and the thickness.
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Radiation attenuation through shielding
Gamma radiation and X-rays behave in a way that sets them apart from alpha and beta particles: they have no definite range at which they abruptly stop. Instead they are attenuated exponentially — each layer of material removes a fixed fraction of what reaches it, but in theory the beam never falls to zero. The law is I = I₀·e^(−μ·x), where I₀ is the intensity entering the shield, μ the linear attenuation coefficient of the material (which depends on both the material and the energy of the radiation) and x the thickness. That has a deep practical consequence: no shield blocks 100% of a gamma beam — you only bring it down to an acceptable level, which is where the idea of the half-value layer comes from. Dense materials (lead, tungsten, barite concrete) have a high μ and therefore shield with less thickness. This calculation underpins the design of radiology rooms, radiotherapy bunkers and shielding for industrial sources. Enter the initial intensity, the attenuation coefficient and the thickness.
Related Tools
Half-Value Layer (HVL)
Compute the half-value layer (HVL), HVL = ln(2)/μ, the material thickness that reduces the radiation intensity by half, from the linear attenuation coefficient (μ). It is the practical way to specify shielding: one HVL cuts 50% of the radiation, two HVLs cut 75%, and so on. Dense materials like lead have a small HVL. Enter the linear attenuation coefficient.
Inverse Square Law (Radiation)
Compute the radiation intensity at a new distance from a point source, I₂ = I₁·(d₁/d₂)², by the inverse square law: intensity falls with the square of distance. Doubling the distance reduces the dose to a quarter — which is why distance is one of the three basic radiation-protection defenses (time, distance and shielding) and the most effective and cheapest. Enter the initial intensity and distance and the new distance.
Gamma Exposure Rate
Compute the exposure (or dose) rate of a point gamma source, X = Γ·A/d², from the exposure-rate constant (Γ, specific to the radionuclide), the source activity (A) and the distance (d). It combines the source strength with the inverse square law, allowing you to estimate the dose received at a given distance — fundamental in planning tasks with radioactive sources. Enter the gamma constant, the activity and the distance.
Collective Dose
Compute the collective dose, S = mean individual dose · number of people, in person-sievert (person-Sv), summing the dose received by an entire exposed group. It is the quantity used to assess the total impact of an exposure on a population — in radiation protection, practice optimization and epidemiological studies. Even small individual doses, multiplied by many people, produce a significant collective dose. Enter the mean individual dose and the number of people.
Number of Half-Lives
Compute how many half-lives have elapsed, n = t/T½, and the fraction of radioactive material remaining, (1/2)ⁿ, from the elapsed time and the half-life. With each half-life the amount halves: after 1 half-life 50% remains, after 2 it is 25%, after 10 less than 0.1%. It is the intuitive way to assess how much of a source (or contamination) is left. Enter the elapsed time and the half-life.
Radioactive Activity
Compute the activity of a radioactive sample, A = λ·N, the product of the decay constant (λ) and the number of radioactive nuclei present (N). Activity, measured in becquerel (Bq = 1 disintegration/s) or curie, expresses how many nuclei decay per second. It is the fundamental quantity quantifying a radioactive source, and it decreases over time as nuclei decay. Enter the decay constant and the number of nuclei.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.