1. Given data

• Number of molecules striking per second: $n = 10^{22}\ \text{s}^{-1}$
• Mass of each molecule: $m = 10^{-26}\ \text{kg}$
• Speed of each molecule: $v = 10^4\ \text{m/s}$
• Area: $A = 1\ \text{m}^2$

The molecules strike the surface perpendicularly and elastically.

2. Change in momentum of one molecule

Since the collision is elastic and perpendicular, the velocity reverses direction.

Initial momentum: $p_i = mv$

Final momentum: $p_f = -mv$

So change in momentum of one molecule is: $\Delta p = p_f - p_i = -mv - mv = -2mv$

Magnitude of change in momentum: $|\Delta p| = 2mv$

Substitute values: $|\Delta p| = 2 \times 10^{-26} \times 10^4 = 2 \times 10^{-22}\ \text{kg m/s}$

3. Force exerted on the surface

Force is rate of change of momentum: $F = n \cdot |\Delta p|$

Thus, $F = 10^{22} \times 2 \times 10^{-22} = 2\ \text{N}$

4. Pressure on the surface

Pressure is force per unit area: $P = \frac{F}{A}$

Since $A=1\ \text{m}^2$, $P = \frac{2}{1} = 2\ \text{N/m}^2$

5. Match with options

The pressure is of the order of: $2\ \text{N/m}^2$

So the correct option is: D: $2\ \text{N/m}^2$

6. Comparison with stored answer

Stored correct answer: D

My derived answer: D

They match.