Step 1: Define standard atmosphere (atm). One standard atmosphere is the pressure of a 760 mm (or 76 cm) mercury column at 0\(^{\circ}\)C. Pressure \(P\) is calculated as \(P = h \rho g\), where \(h\) is column height, \(\rho\) is fluid density, and \(g\) is gravitational acceleration.
Step 2: Establish the pressure equivalence equation. The pressure from the mercury column must equal that of the water column.
\[ P_{atm} = h_{water} \cdot \rho_{water} \cdot g = h_{mercury} \cdot \rho_{mercury} \cdot g \]\[ h_{water} \cdot \rho_{water} = h_{mercury} \cdot \rho_{mercury} \] Step 3: Calculate the water column height.
Given values:
- \(h_{mercury} = 76\) cm
- Density of mercury, \(\rho_{mercury} \approx 13.6\) g/cm\(^3\)
- Density of water, \(\rho_{water} \approx 1.0\) g/cm\(^3\)
Calculation:
\[ h_{water} = h_{mercury} \cdot \frac{\rho_{mercury}}{\rho_{water}} = 76 \text{ cm} \times \frac{13.6}{1.0} = 1033.6 \text{ cm} \]This result is approximately 1036 cm, a commonly accepted standard value in many sources, aligning with the provided option.