For some of these problems, you'll need to make use of the simple differential equation: dY = -kY, where k is a constant. The solution to this differential equation is Y(x) = Y, e-kx, where Y, is the value of Y at x = 0. dx 4. Experiments in surface science are normally carried out in vacuum chambers at extremely low pressures to prevent the surface from becoming quickly contaminated by stray molecules. Estimate how low the pressure (in bar) must be if a square patch of 10.0 nm on a side is to suffer on average fewer than one collision per hour when the temperature is 298 K. Assume the chief contaminant is air and that its molecules have an average speed (v) of 650 ms-1 and collision cross section of 37 P. (The surface is stationary, so you should use (v) instead of (VAA).) For some of these problems, you'll need to make use of the simple differential equation: dY = -kY, where k is a constant. The solution to this differential equation is Y(x) = Y, e-kx, where Y, is the value of Y at x = 0. dx 4. Experiments in surface science are normally carried out in vacuum chambers at extremely low pressures to prevent the surface from becoming quickly contaminated by stray molecules. Estimate how low the pressure (in bar) must be if a square patch of 10.0 nm on a side is to suffer on average fewer than one collision per hour when the temperature is 298 K. Assume the chief contaminant is air and that its molecules have an average speed (v) of 650 ms-1 and collision cross section of 37 P. (The surface is stationary, so you should use (v) instead of (VAA).)