Lesson 3 ◆ Tutorial

Q: Calculate the specific activity (Bq/g) of natural UO2_2 fuel and compare it with the specific activity of 3.5% enriched UO2_2 calculated in Section 3.6.

A:

Step 1: Mass fraction of uranium in UO2_2

fU=238270=0.8815f_U = \frac{238}{270} = 0.8815

In 1 g of natural UO2_2, the mass of uranium is 0.8815 g.

Step 2: Mass of each isotope in 1 g of natural UO2_2

  • U-234: Weight fraction 0.0055%; mass in 1 g UO2_2 = 0.8815 ×\times 5.5 ×\times 10−5^{-5} = 4.85 ×\times 10−5^{-5} g
  • U-235: Weight fraction 0.720%; mass in 1 g UO2_2 = 0.8815 ×\times 7.2 ×\times 10−3^{-3} = 6.35 ×\times 10−3^{-3} g
  • U-238: Weight fraction 99.275%; mass in 1 g UO2_2 = 0.8815 ×\times 0.99275 = 8.751 ×\times 10−1^{-1} g

Step 3: Activity of each isotope

Using A=ln⁡2T1/2×m×NAMA = \frac{\ln 2}{T_{1/2}} \times \frac{m \times N_A}{M} and the decay constants from the earlier worked example:

U-234:

A234=8.93×10−14×4.85×10−5×6.022×1023234=8.93×10−14×1.249×1017=1.12×104 BqA_{234} = 8.93 \times 10^{-14} \times \frac{4.85 \times 10^{-5} \times 6.022 \times 10^{23}}{234} = 8.93 \times 10^{-14} \times 1.249 \times 10^{17} = 1.12 \times 10^{4} \text{ Bq}

U-235:

A235=3.12×10−17×6.35×10−3×6.022×1023235=3.12×10−17×1.626×1019=5.07×102 BqA_{235} = 3.12 \times 10^{-17} \times \frac{6.35 \times 10^{-3} \times 6.022 \times 10^{23}}{235} = 3.12 \times 10^{-17} \times 1.626 \times 10^{19} = 5.07 \times 10^{2} \text{ Bq}

U-238:

A238=4.92×10−18×8.751×10−1×6.022×1023238=4.92×10−18×2.214×1021=1.09×104 BqA_{238} = 4.92 \times 10^{-18} \times \frac{8.751 \times 10^{-1} \times 6.022 \times 10^{23}}{238} = 4.92 \times 10^{-18} \times 2.214 \times 10^{21} = 1.09 \times 10^{4} \text{ Bq}

Step 4: Total

Atotal=1.12×104+5.07×102+1.09×104≈2.26×104 Bq/gA_{\text{total}} = 1.12 \times 10^4 + 5.07 \times 10^2 + 1.09 \times 10^4 \approx 2.26 \times 10^4 \text{ Bq/g}

Comparison:

  • Natural UO2_2: Specific activity ~2.3 ×\times 104^4 Bq/g (ratio: 1.0)
  • 3.5% enriched UO2_2: Specific activity ~6.7 ×\times 104^4 Bq/g (ratio: ~3)

The enriched fuel has approximately 3 times the specific activity of natural fuel. This is mainly because enrichment increases the U-234 content disproportionately (from 0.0055% to ~0.027%), and U-234 is the dominant contributor to activity.