The energy of the van der Waals bond, which is responsible...

The energy of the van der Waals bond, which is responsible for a number of the characteristics of water, is about $0.50 \mathrm{eV}$. (a) At what temperature would the average translational kinetic energy of water molecules be equal to this energy? (b) At that temperature, would water be liquid or gas? Under ordinary everyday conditions, do van der Waals forces play a role in the behavior of water?

Key Concepts

Electron Transitions and Photon Absorption

When an electron transitions between energy levels, it absorbs or emits a photon with an energy equal to the difference between the initial and final energy states. This principle allows us to calculate the wavelength of the absorbed or emitted light using the relationship E = hc/?. Such transitions are fundamental in understanding atomic spectra and the mechanisms underlying excitation processes.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all wavelengths of electromagnetic radiation, with the visible spectrum ranging approximately from 400 nm to 700 nm. Whether a photon is visible to the human eye depends on its wavelength. In atomic transitions, the resulting photon may fall outside of this range (for example, in the ultraviolet or infrared regions), which is critical to identifying the nature of the light involved in electron transitions.

Hydrogen Atom Energy Levels

The energy levels of the hydrogen atom are quantized, meaning that an electron can only occupy specific energy states. These levels are typically indexed by the principal quantum number n, and the energy associated with each level is inversely proportional to n². This concept is essential for understanding electron configurations and the quantized nature of atomic systems.

Quantization of Angular Momentum

Orbital angular momentum in quantum mechanics is also quantized. For a given principal quantum number n, the orbital angular momentum quantum number l can take on integer values from 0 up to n – 1. The magnitude of the orbital angular momentum is given by ?[l(l+1)] times the reduced Planck constant (?). This quantization is key to explaining the discrete magnetic and spectral properties of atoms.

Transcript

00:01 Okay, so in this question, we know that an electron in hydrogen has an energy of 0 .544 ev.

00:16 And we also, and we want to know, i guess, what are the possible values of orbital, angular momentum.

00:24 Well, we need to find the n, the principal quantum number for this electron.

00:30 And so we can do that based on information in the other chapter, the previous chapter, which says that the energy levels in the hydrogen spectrum are negative 13 .6 over n squared.

00:42 So if we plug this in for e and solve for n, we would get n equals 5.

00:47 So that means that little l can equal 0, 1, 2, 3, 4, all the way up to n minus 1.

01:00 And so we want to get the possible values of orbital angular momentum in terms of h -bar.

01:05 So we just want to use this l equals the square root of l times l plus 1.

01:13 And so there are 4 times h bar.

01:16 And so the possible values are l.

01:19 If you plug in 0, you'll get 0.

01:22 If you plug in 1, you'll get the square root of 2.

01:25 And if you plug in 2, you'll get square root of 6.

01:32 If you plug in 3, you'll get the square root of 12.

01:36 And if you plug in 4, you'll get the square root of 20.

01:42 And then that's all in units of age bar...