Manual Calculation:
Given:
• Mass of Top Quark (m): 3.0916×10−253.0916 \times 10^{-25}3.0916×10−25 kg
• Mass Uncertainty (Δm): 0.3 GeV/c²
Conversion to kg:
• Conversion factor: 1 GeV/c2=1.78266192×10−27 kg1 \, \text{GeV}/c^2 = 1.78266192 \times 10^{-27} \, \text{kg}1GeV/c2=1.78266192×10−27kg
• Mass Uncertainty in kg: 0.3 GeV/c2×1.78266192×10−27 kg/GeV/c2=5.34798576×10−28 kg0.3 \, \text{GeV}/c^2 \times 1.78266192 \times 10^{-27} \, \text{kg/GeV}/c^2 = 5.34798576 \times 10^{-28} \, \text{kg}0.3GeV/c2×1.78266192×10−27kg/GeV/c2=5.34798576×10−28kg
Certainty and Uncertainty Calculation:
• Certainty Percentage: (1−UncertaintyValue)×100%\left(1 - \frac{\text{Uncertainty}}{\text{Value}}\right) \times 100\%(1−ValueUncertainty)×100%
o Certainty = (1−5.34798576×10−283.0916×10−25)×100%≈99.827%\left(1 - \frac{5.34798576 \times 10^{-28}}{3.0916 \times 10^{-25}}\right) \times 100\% \approx 99.827\%(1−3.0916×10−255.34798576×10−28)×100%≈99.827%
• Uncertainty Percentage: UncertaintyValue×100%\frac{\text{Uncertainty}}{\text{Value}} \times 100\%ValueUncertainty×100%
o Uncertainty = 5.34798576×10−283.0916×10−25×100%≈0.173%\frac{5.34798576 \times 10^{-28}}{3.0916 \times 10^{-25}} \times 100\% \approx 0.173\%3.0916×10−255.34798576×10−28×100%≈0.173%
Thus, the uncertainty percentage for the Top Quark's mass is approximately 0.173%, and the certainty percentage is 99.827%. This indicates a high precision in the measurement of the Top Quark's mass.
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