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Radiation Physics

Radiation Shielding Calculator — HVL & TVL

Beer-Lambert law with buildup factor for gamma, beta, and neutron shielding. Computes HVL, TVL, transmitted intensity, and dose rate in real time for lead, concrete, water, iron, and polyethylene.

Parameters
Radiation Type
Shielding Material
Photon energy E1.00 MeV
Source activity A100 MBq
Shield thickness x10.0 cm
Distance r1.00 m
HVL [cm]
TVL [cm]
Transmission I/I₀ [%]
Shielding effect [%]
μ/ρ [cm²/g]
Linear μ [1/cm]
Dose rate before [μSv/h]
Dose rate after [μSv/h]
Transmitted Intensity vs Shield Thickness (log scale)

Beer-Lambert Law & Shielding Theory

Gamma-ray transmitted intensity (with buildup correction):

$$I = I_0 \cdot B(\mu x) \cdot \exp(-\mu \rho x)$$

where $\mu/\rho$: mass attenuation coefficient [cm²/g], $\rho$: density [g/cm³], $x$: thickness [cm]. $B$: buildup factor (scatter correction, $B \geq 1$).

HVL: $\dfrac{\ln 2}{\mu} = \dfrac{0.693}{\mu}$, TVL: $\dfrac{\ln 10}{\mu} = \dfrac{2.303}{\mu}$

Distance attenuation (inverse-square law): $\dot{D}(r) \propto \dfrac{1}{r^2}$

Applications: Shielding design for nuclear facilities, radiotherapy rooms, and RI labs. Hand-calculation verification for MCNP and SHIELD-11 results. Dose rate assessment per ICRP Publication 116. Numerical demonstration of the ALARA principle (time, distance, shielding).