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\(\text{Na} \to \text{Na}^+ + e^-\): requires IEβ = +5.1 eV (energy absorbed)
Electron gain enthalpy of NaβΊ is the reverse process:
\(\text{Na}^+ + e^- \to \text{Na}\): releases the same energy
\(\Delta_{\text{eg}}H(\text{Na}^+) = -5.1\) eV
This follows Hess's law β the reverse process has equal and opposite enthalpy.
Find the count of natural numbers less than $7000$ that can be formed using the digits $0, 1, 3, 7, 9$ with repetition allowed.
1-digit: $1, 3, 7, 9$ (excluding 0) $= 4$
2-digit: First digit: 4 choices (1,3,7,9); second: 5 choices $= 4 \times 5 = 20$
3-digit: First digit: 4 choices; others: 5 each $= 4 \times 5 \times 5 = 100$
4-digit $< 7000$: First digit must be $1$ or $3$ (2 choices, since 7000 and above excluded β first digit can be 1, 3 only for $< 7000$; digits 7 and 9 give $\geq 7000$): $2 \times 5 \times 5 \times 5 = 250$
Total $= 4 + 20 + 100 + 250 = \mathbf{374}$
Complete the analogy: Order is the law of civilization as chaos is the law of the ______.
This is a classic contrast: civilization represents order, while the wilderness (nature untamed) represents chaos. The phrase evokes the idea that human society creates order, whereas wild nature is chaotic.
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