The order of magnitude of the threshold temperature.

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Chapter 44, Problem 44AP

To determine

The order of magnitude of the threshold temperature.

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In solid helium the spacing between atoms is about 3Å . Helium contains 2 protons and 2 neutrons, so the mass of a helium atom is 6.6×10−27 kg. What is the smallest possible energy of a helium atom in solid helium? What temperature (in Kelvin) does this energy correspond with? (Boltzmann's constant is kb=1.38×10−23 J/K

(b) Calculate the half width in nanometers for Doppler broadening of the 4s S 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculatedin (e). (g) Create a spreadsheet to calculate the Doppler half width DlD in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.

A molecule in Earth's atmosphere at 20 °C has a most probable energy E = kT/2 = 2.02 ×10-21 J E = kT =4.04 ×10-21 J E = 3 k T / 2 = 6.1 ×10-21 J that depends on the mass of the molecule