Radioactive sodium-24, administered as 2"NaCl, is given to treat leukemia. If a patient must receive 190 µCi/kg and the isotope is supplied as a solution that contains 4.0 mCi/mL, what volume is needed for a 70.-kg patient?

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**Title: Dosage Calculation for Radioactive Sodium-24 Treatment**

**Problem Statement:**

Radioactive sodium-24, administered as \(^{24}\text{NaCl}\), is used in the treatment of leukemia. If a patient must receive a dosage of 190 \( \mu \text{Ci/kg} \) and the isotope is available in a solution with a concentration of 4.0 \( \text{mCi/mL} \), what volume of solution is required for a patient weighing 70 kg?

**Solution Process:**

1. **Determine the Total Activity Required for the Patient:**
   - Patient weight = 70 kg
   - Required dosage = 190 \( \mu \text{Ci/kg} \)
   - Total activity needed = \( 70 \text{ kg} \times 190 \mu \text{Ci/kg} \)

2. **Convert the Total Activity to mCi:**
   - Note: \(1 \text{ mCi} = 1000 \mu \text{Ci}\)
   - Convert the total activity required from \( \mu \text{Ci} \) to \( \text{mCi} \).

3. **Calculate the Volume of Solution:**
   - Concentration of the solution = 4.0 \( \text{mCi/mL} \)
   - Use the formula: 
     \[
     \text{Volume (mL)} = \frac{\text{Total Activity (mCi)}}{\text{Concentration (mCi/mL)}}
     \]
   - Calculate the volume of solution needed.

**Additional Notes:**

- Ensure all units are consistent during calculations.
- Verify calculations to maintain treatment accuracy.

**Interactive Features:**

- **Check My Work**: An option to verify the correctness of the calculated answer.
- **Hint**: Provides guidance on approaching the solution.
- **Solution**: Shows the complete step-by-step solution to the problem.
- **Guided Solution**: Offers detailed guidance and explanations for each step, ideal for learning purposes.

**Note**: Understanding how to perform unit conversions and calculate dosages accurately is crucial in medical treatments involving radioactive materials.
Transcribed Image Text:**Title: Dosage Calculation for Radioactive Sodium-24 Treatment** **Problem Statement:** Radioactive sodium-24, administered as \(^{24}\text{NaCl}\), is used in the treatment of leukemia. If a patient must receive a dosage of 190 \( \mu \text{Ci/kg} \) and the isotope is available in a solution with a concentration of 4.0 \( \text{mCi/mL} \), what volume of solution is required for a patient weighing 70 kg? **Solution Process:** 1. **Determine the Total Activity Required for the Patient:** - Patient weight = 70 kg - Required dosage = 190 \( \mu \text{Ci/kg} \) - Total activity needed = \( 70 \text{ kg} \times 190 \mu \text{Ci/kg} \) 2. **Convert the Total Activity to mCi:** - Note: \(1 \text{ mCi} = 1000 \mu \text{Ci}\) - Convert the total activity required from \( \mu \text{Ci} \) to \( \text{mCi} \). 3. **Calculate the Volume of Solution:** - Concentration of the solution = 4.0 \( \text{mCi/mL} \) - Use the formula: \[ \text{Volume (mL)} = \frac{\text{Total Activity (mCi)}}{\text{Concentration (mCi/mL)}} \] - Calculate the volume of solution needed. **Additional Notes:** - Ensure all units are consistent during calculations. - Verify calculations to maintain treatment accuracy. **Interactive Features:** - **Check My Work**: An option to verify the correctness of the calculated answer. - **Hint**: Provides guidance on approaching the solution. - **Solution**: Shows the complete step-by-step solution to the problem. - **Guided Solution**: Offers detailed guidance and explanations for each step, ideal for learning purposes. **Note**: Understanding how to perform unit conversions and calculate dosages accurately is crucial in medical treatments involving radioactive materials.
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