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

Question

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

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Solution

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=I0(12)dHVL I = I_0 \left( \frac{1}{2} \right)^{\frac{d}{\text{HVL}}}

where:

  • II is the intensity of the radiation after passing through the material,
  • I0I_0 is the initial intensity of the radiation,
  • dd is the thickness of the material,
  • HVL\text{HVL} is the half-value layer.

3. Analysis and Detail

  1. Given data:

    • Thickness of the material d=6 cmd = 6 \text{ cm}
    • Half-Value Layer HVL=2 cm\text{HVL} = 2 \text{ cm}
  2. Plug the values into the formula to find the intensity after passing through: I=I0(12)62=I0(12)3 I = I_0 \left( \frac{1}{2} \right)^{\frac{6}{2}} = I_0 \left( \frac{1}{2} \right)^{3}

  3. Calculate (12)3\left( \frac{1}{2} \right)^{3}: (12)3=18 \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=I0×18 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: Percentage=(II0)×100%=18×100%=12.5% \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%.

This problem has been solved

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