In an ultrahigh vacuum chamber (P=5 ×10^-10 torr ) how many molecules strike 1 cm^2 of surface i

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In an ultrahigh vacuum chamber (P=5 ×10^-10 torr ) how many...

In an ultrahigh vacuum chamber $\left(P=5 \times 10^{-10} \text {torr }\right)$ how many molecules strike $1 \mathrm{cm}^{2}$ of surface in one second at 298 $\mathrm{K}$ if $(a)$ the gas is helium and $(b)$ the gas is mercury vapor?

Key Concepts

Effect of Molecular Mass on Speed

Molecular mass plays a vital role in determining the speed of gas molecules for a given thermal energy. According to kinetic theory, lighter molecules (like helium) will, on average, move faster than heavier molecules (such as mercury vapor) at the same temperature. This difference in speed results in varying rates of molecular impacts on surfaces, even under identical pressure and temperature conditions.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution describes the spread of molecular speeds in a gas at a given temperature. It is critical because it enables the computation of average speeds of the molecules, which is necessary for determining the flux of molecules hitting a surface. This distribution explains how, even at a fixed temperature, molecules exhibit a range of velocities.

Kinetic Theory of Gases

Kinetic theory provides the framework for understanding the macroscopic properties of gases by considering their molecular motion. It explains how temperature relates to the average kinetic energy and speed of the molecules. This theory underpins the calculations of molecular collision rates with surfaces as it incorporates the effects of temperature and molecular mass on speeds.

Ideal Gas Law

The ideal gas law (PV = NkT) connects the pressure, volume, number of molecules, and temperature of a gas. In applications such as calculating molecular collisions in a vacuum, it allows for the determination of the number density of gas molecules from a known pressure and temperature, which is essential for subsequent kinetic computations.

Molecular Flux

Molecular flux represents the number of gas molecules striking a unit area of a surface per unit time. In kinetic gas theory, it is typically calculated using the expression (n * ?v?/4), where n is the number density of the gas and ?v? is the average molecular speed. This concept is central to understanding surface interactions in vacuum conditions.

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