Let's analyze the question which asks which of the given options cannot be used to express standard atmospheric pressure. Standard atmospheric pressure is a measure of the force exerted by the weight of the air above a unit area of the Earth's surface. Pressure is fundamentally defined as force per unit area.

Understanding Units of Pressure

Pressure units typically involve a unit of force divided by a unit of area. Let's examine each option provided:

• Option 1: 760 mm Hg

This unit represents the height of a column of mercury (Hg) that the atmospheric pressure can support at standard conditions. This is a common way to express pressure, especially in older systems and barometry. The pressure exerted by a fluid column is given by the formula $\text{P} = \rho \text{gh}$, where $\rho$ is the density of the fluid, $\text{g}$ is the acceleration due to gravity, and $\text{h}$ is the height of the column. Since the density of mercury and gravity are constants at a specific location, the height of the mercury column is directly proportional to the pressure. Therefore, 760 mm Hg is a valid way to express standard atmospheric pressure.

• Option 2: 1.03 Kg Wt /cm$\text{^{2}}$

Kg Wt (kilogram weight) is a unit of force. 1 Kg Wt is the force exerted by a mass of 1 kg due to gravity, approximately equal to 9.8 Newtons. cm$\text{^{2}}$ is a unit of area. So, Kg Wt /cm$\text{^{2}}$ represents force per unit area, which is the definition of pressure. This unit is often used in technical contexts. Converting it to Pascal (Pa):

$1.03 \text{ Kg Wt} / \text{cm}^{2} \approx 1.03 \times 9.8 \text{ N} / (10^{-2} \text{ m})^{2}$

$\approx 1.03 \times 9.8 \text{ N} / 10^{-4} \text{ m}^{2}$

$\approx 10.094 \times 10^{4} \text{ N/m}^{2}$

$\approx 100940 \text{ Pa} \approx 100.94 \text{ kPa}$

This value is very close to the standard atmospheric pressure (101.3 kPa). So, this is a valid unit for expressing pressure.

• Option 3: 101.3 Kilo Pascal

Pascal (Pa) is the SI unit of pressure, defined as one Newton per square meter (N/m$\text{^{2}}$). Kilo Pascal (kPa) is 1000 Pascals. 101.3 kPa is the internationally accepted standard value for atmospheric pressure at sea level under standard conditions. This is a standard and correct way to express standard atmospheric pressure.

• Option 4: 1.03 Kg Wt. /cm$\text{^{3}}$

Kg Wt (kilogram weight) is a unit of force. cm$\text{^{3}}$ is a unit of volume. The unit Kg Wt. /cm$\text{^{3}}$ represents force per unit volume. This is not a unit of pressure (Force/Area). This unit represents a quantity known as force density or weight density (weight per unit volume). Pressure is always force per unit area.

Conclusion

Based on the analysis of units, the unit Kg Wt. /cm$\text{^{3}}$ represents force per unit volume (force density or weight density), not force per unit area (pressure). Therefore, this unit cannot be used to express standard atmospheric pressure.

The options that correctly express standard atmospheric pressure are 760 mm Hg, 1.03 Kg Wt /cm$\text{^{2}}$, and 101.3 Kilo Pascal. The option that cannot express standard atmospheric pressure is 1.03 Kg Wt. /cm$\text{^{3}}$.