Final answer:
The minimum density of molecules required for PALM is directly proportional to the pressure and can be reduced by reducing the pressure by half.
Step-by-step explanation:
The minimum density of molecules required for PALM can be determined using the ideal gas law and Avogadro's number. First, we need to calculate the number of molecules by multiplying the number of moles (n) by Avogadro's number (N₁). Then, we can use the ideal gas law to calculate the number density (N/V) of the gas.
Using Avogadro's number, N = nN₁ = (1.14 × 10-4 mol) (6.02 × 1023 molecules/mol) = 6.85 × 1019 molecules.
From the ideal gas law, N/V = p/kB T, where p is the pressure, kB is the Boltzmann constant, and T is the temperature. Therefore, if the density (and number density) is reduced by half, the pressure must also be reduced by half.
Thus, the minimum density of molecules required for PALM is directly proportional to the pressure and can be reduced by reducing the pressure by half.