Model-based estimate. Use the stated geometry, composition and measurement assumptions; see the tool scope for limitations.

Input

Beta source and shield material

Calculation mode

Beta source

E_max, MeV

Shield material

Lower Z gives less bremsstrahlung — shield beta with plastic/aluminium, not lead.

AssumptionsFraction of beta energy converted to bremsstrahlung at full absorption in the material.Evans f = Z·E_max/3000 (beta standard); ICRU is a physically refined alternative.Gives the energy fraction, not an absolute dose; secondary photon spectrum is not modeled.

Result

Bremsstrahlung energy fraction

6.232%

Fraction (Evans): 6.232%
Fraction (ICRU): 10.086%
Z_eff: 82
E_max: 2.28 MeV

Bremsstrahlung and X-ray Tube

Bremsstrahlung fraction estimate

The calculator estimates the fraction of beta energy converted to bremsstrahlung X-rays when absorbed in a shield material. It uses the Evans formula f = Z·E_max/3000 (the beta-spectrum standard) and the ICRU/Seltzer-Berger approximation. The higher the effective atomic number Z, the more bremsstrahlung — which is why beta emitters are shielded with light materials (acrylic, aluminium), not lead.

X-ray tube dose rate

The second mode is an order-of-magnitude estimate of the X-ray tube dose rate from the voltage (kVp), current (mA) and distance. A tungsten-anode tube output grows roughly as the square of the voltage, and the dose falls off as the inverse square of distance. Air-kerma gamma factors are taken from the literature (Campillo-Rivera 2021, DIN 54113-3).

Accuracy and limitations

Important: the real tube output depends on design and filtration and may differ from the estimate by a factor of 10–50, so the result is an order of magnitude, not an exact value. For safety decisions use the certificate and calibration of the specific tube.