Lead is a good absorber of X rays. Specific gravity of `Pb = 11.5`. To cut down the initial radiation `l_(0)` to `(l_(0))/(2)` a shield of `1.5 cm` was used. The mass absorption co-efficient is

Options

A. `0.06 cm^(2)//g`
B. `0.462 cm^(-1)`
C. `0.21 cm^(-1)`
D. `0.040 cm^(2)//g`

Explanation

To find the mass absorption coefficient of lead (Pb) given the specific gravity and the thickness of the shield used to reduce the intensity of X-rays, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the mass absorption coefficient (μ) of lead when the initial radiation intensity \( l_0 \) is reduced to \( \frac{l_0}{2} \) using a shield of thickness \( x = 1.5 \, \text{cm} \).

2. **Use the Exponential Attenuation Formula**: The intensity of radiation after passing through a material is given by:
\[ l = l_0 e^{-\mu x} \]
where:
- \( l \) is the final intensity,
- \( l_0 \) is the initial intensity,
- \( \mu \) is the mass absorption coefficient,
- \( x \) is the thickness of the material.

3. **Set Up the Equation**: Since we want to reduce the intensity to half, we can set:
\[ \frac{l_0}{2} = l_0 e^{-\mu x} \]

4. **Cancel \( l_0 \)**: Dividing both sides by \( l_0 \) (assuming \( l_0 \neq 0 \)):
\[ \frac{1}{2} = e^{-\mu x} \]

5. **Take the Natural Logarithm**: Taking the natural logarithm of both sides:
\[ \ln\left(\frac{1}{2}\right) = -\mu x \]

6. **Simplify the Left Side**: We know that \( \ln\left(\frac{1}{2}\right) = -\ln(2) \):
\[ -\ln(2) = -\mu x \]
Thus, we can simplify to:
\[ \mu x = \ln(2) \]

7. **Solve for \( \mu \)**: Rearranging gives:
\[ \mu = \frac{\ln(2)}{x} \]

8. **Substitute the Value of \( x \)**: Now, substitute \( x = 1.5 \, \text{cm} \):
\[ \mu = \frac{\ln(2)}{1.5} \]

9. **Calculate \( \ln(2) \)**: We know that \( \ln(2) \approx 0.693 \):
\[ \mu = \frac{0.693}{1.5} \]

10. **Final Calculation**: Performing the division:
\[ \mu \approx 0.462 \, \text{cm}^{-1} \]

### Conclusion:
The mass absorption coefficient \( \mu \) of lead is approximately \( 0.462 \, \text{cm}^{-1} \).