Relation Cross-Scans

Weighted Energy Contribution Cross-Scan

The average-energy numerator is built from three visible weighted terms. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Energy contribution row 1

Energy 0 times weight 4 contributes 0 joules to the numerator.

1⋅0⋅4=01\cdot 0\cdot 4=0
Weighted energy row 1Each row is one term of the checked average-energy numerator.E=0, weight=4, contribution=0

Energy contribution row 2

Energy 2 times weight 2 contributes 4 joules to the numerator.

1⋅2⋅2=41\cdot 2\cdot 2=4
Weighted energy row 2Each row is one term of the checked average-energy numerator.E=2, weight=2, contribution=4

Energy contribution row 3

Energy 4 times weight 1 contributes 4 joules to the numerator.

1⋅4⋅1=41\cdot 4\cdot 1=4
Weighted energy row 3Each row is one term of the checked average-energy numerator.E=4, weight=1, contribution=4

All weighted terms make the average-energy numerator

The three contributions sum to eight joules. Dividing by the same partition total seven gives the average energy eight sevenths of a joule.

⟨E⟩=0+4+47=87\langle E\rangle=\frac{0+4+4}{7}=\frac{8}{7}
Weighted energy contribution cross-scanThe numerator is shown as three exact source-bound terms.0 + 4 + 4 over Z=7 gives average energy 8/7