• H⁺ (Z=1): 0 electrons
• Li⁺ (Z=3): 2 electrons ✓ — isoelectronic with Be²⁺
• Na⁺ (Z=11): 10 electrons
• Mg²⁺ (Z=12): 10 electrons

Calculate each value:

• Column A: $3^4 = 81$
• Column B: $4^3 = 64$

Since $81 > 64$, Column A is greater. However, checking the answer choices in the original problem shows this is actually option C (equal) as marked. Let me recalculate: $3^4 = 3 \times 3 \times 3 \times 3 = 81$ and $4^3 = 4 \times 4 \times 4 = 64$. These are NOT equal. The correct answer based on calculation is that Column A is greater.

Upon reviewing the source material, the answer appears to be that the two are NOT equal, so Column A ($3^4 = 81$) is greater than Column B ($4^3 = 64$).

$v = \dfrac{ds}{dt} = 3t^2 - 12t + 3$

$a = \dfrac{dv}{dt} = 6t - 12$

Setting $a = 0$: $t = 2\text{ s}$

$v\big|_{t=2} = 3(4) - 12(2) + 3 = 12 - 24 + 3 = \mathbf{-9\text{ m/s}}$

At the point of precipitation: $[\text{Ba}^{2+}][\text{SO}_4^{2-}] = K_{sp} = 1 \times 10^{-10}$

Find $[\text{SO}_4^{2-}]$ in the final mixture:

Moles of SO$_4^{2-}$ added $= 0.050\ \text{L} \times 1\ \text{M} = 0.05\ \text{mol}$

Final volume $= 500\ \text{mL} = 0.5\ \text{L}$

$[\text{SO}_4^{2-}]_{\text{final}} = \dfrac{0.05}{0.5} = 0.1\ \text{M}$

Find $[\text{Ba}^{2+}]$ in the final mixture:

$[\text{Ba}^{2+}]_{\text{final}} = \dfrac{K_{sp}}{[\text{SO}_4^{2-}]} = \dfrac{1\times10^{-10}}{0.1} = 1\times10^{-9}\ \text{M}$

Back-calculate original concentration: Final volume is 10× original Ba$^{2+}$ volume (500 mL total, 450 mL original solution).

Original $[\text{Ba}^{2+}] = 1\times10^{-9} \times \dfrac{500}{450} \approx \mathbf{2\times10^{-9}}\ \text{M}$

The Glasgow Coma Scale (GCS) scoring:

Calculation: E + V + M = 2 + 2 + 3 = 7

Interpretation: GCS 3–8 = Severe brain injury (coma), GCS 9–12 = Moderate, GCS 13–15 = Mild/Normal. A GCS ≤ 8 typically indicates need for airway protection (intubation).