Question

The collision flux of a monoatomic gas on copper surface is \(3.0 \times 10^{18}\) m\(^-2\) s\(^{-1}\). Note that copper surface forms a square lattice with lattice constant of 210 pm. If the sticking coefficient of the atom with copper is 1.0, the time taken by the gas to form a complete monolayer on the surface is ................ s. (Round off to one decimal place)

Hint:

To find the time for a gas to form a monolayer on a surface, divide the total number of available sites by the collision flux. The number of sites is calculated using the lattice constant and the surface area of the unit cell.

Answer 1

Correct Answer: 7.5

Step 1: Calculate the number of sites on the copper surface.
The surface area of each unit cell on the copper surface is given by the square of the lattice constant. For copper, the lattice constant is 210 pm. The area of one unit cell is: \[ A_{\text{cell}} = (210 \, \text{pm})^2 = 44,100 \, \text{pm}^2 = 44.1 \times 10^{-18} \, \text{m}^2 \] The number of sites per square meter on the copper surface is the inverse of the area of one unit cell: \[ \text{Sites per square meter} = \frac{1}{A_{\text{cell}}} = \frac{1}{44.1 \times 10^{-18}} = 2.27 \times 10^{16} \, \text{sites/m}^2 \] Step 2: Calculate the time to form a monolayer.
The time to form a monolayer is the number of sites on the surface divided by the collision flux. The collision flux is given as \(3.0 \times 10^{18} \, \text{m}^{-2} \, \text{s}^{-1}\). \[ \text{Time to form monolayer} = \frac{\text{Number of sites per square meter}}{\text{Collision flux}} = \frac{2.27 \times 10^{16}}{3.0 \times 10^{18}} = 7.57 \times 10^{-3} \, \text{s} \] The time is approximately 1.1 seconds.
Step 3: Conclusion.
Thus, the time taken by the gas to form a complete monolayer on the surface is 1.1 seconds.