What is the factor by which the use of 3 tenth value layers of shielding reduces radiation intensity?

The concept of tenth value layers (TVLs) is crucial in understanding how shielding materials attenuate radiation intensity. A tenth value layer is the thickness of a shielding material required to reduce the intensity of radiation to one-tenth of its original value. When you use multiple layers of shielding, the reduction in intensity is exponential rather than linear.

In the case of three tenth value layers:

1. The first layer reduces the intensity to 1/10 of the original (0.1).

2. The second layer reduces the remaining intensity (0.1) to 1/10 of that value, which results in 0.01 of the original intensity.

3. The third layer reduces this remaining intensity (0.01) to 1/10 of that value, leading to 0.001 of the original intensity.

Mathematically, this is illustrated as follows:

• After the first layer: ( I_1 = I_0 \times \frac{1}{10} )

• After the second layer: ( I_2 = I_1 \times \frac{1}{10} = I_0 \times \frac{1}{10^2} = I_0 \times \frac{1}{