Sinar radioaktif dilewatkan melalui bahan yang tebalnya 6 cm. Jika bahan memiliki HVL = 2 cm , maka persentase sinar radioaktif yang melewati bahan adalah

1. Break Down the Problem

We need to determine the percentage of radioactive rays that pass through a material that is 6 cm thick, given that the Half-Value Layer (HVL) of the material is 2 cm.

2. Relevant Concepts

The relationship between thickness, HVL, and the intensity of radiation can be expressed using the formula:

$I = I_0 \left( \frac{1}{2} \right)^{\frac{d}{\text{HVL}}}$

where:

• $I$ is the intensity of the radiation after passing through the material,
• $I_0$ is the initial intensity of the radiation,
• $d$ is the thickness of the material,
• $\text{HVL}$ is the half-value layer.

3. Analysis and Detail

1. Given data:

   • Thickness of the material $d = 6 \text{ cm}$
   • Half-Value Layer $\text{HVL} = 2 \text{ cm}$

2. Plug the values into the formula to find the intensity after passing through: $I = I_0 \left( \frac{1}{2} \right)^{\frac{6}{2}} = I_0 \left( \frac{1}{2} \right)^{3}$

3. Calculate $\left( \frac{1}{2} \right)^{3}$: $\left( \frac{1}{2} \right)^{3} = \frac{1}{8}$

This means that the intensity of the radioactive rays that passes through the material is: $I = I_0 \times \frac{1}{8}$

4. Verify and Summarize

We find that 1/8 of the initial intensity passes through. To express this as a percentage: $\text{Percentage} = \left( \frac{I}{I_0} \right) \times 100\% = \frac{1}{8} \times 100\% = 12.5\%$

Final Answer

The percentage of radioactive rays that pass through the material is 12.5%.