Arrange the following H atom electron transitions in order...

Arrange the following $\mathrm{H}$ atom electron transitions in order of decreasing wavelength of the photon absorbed or emitted:
(a) $n=2$ to $n=\infty$
(b) $n=4$ to $n=20$
(c) $n=3$ to $n=10$
(d) $n=2$ to $n=1$

Key Concepts

Bohr Model

The Bohr model of the hydrogen atom describes how electrons orbit the nucleus in defined energy levels or shells. Transitions between these levels result in the absorption or emission of photons, with the photon's energy corresponding to the difference between the initial and final energy states.

Energy Level Transitions

Electron transitions in an atom occur when an electron jumps from one quantized energy level to another. The energy difference between these levels determines whether the process requires energy absorption or results in photon emission, with larger differences corresponding to higher energy photons.

Rydberg Formula

The Rydberg formula is used to predict the wavelengths of the photons emitted or absorbed during electron transitions in hydrogen-like atoms. It relates the initial and final energy levels to the wavelength of the photon through a proportionality constant known as the Rydberg constant.

Photon Energy-Wavelength Relationship

The relationship between the energy of a photon and its wavelength is described by the equation E = hc/?, where E is the energy, h is Planck’s constant, c is the speed of light, and ? is the wavelength. This implies that transitions involving a small energy difference will produce photons with longer wavelengths, while larger energy differences yield shorter wavelengths.

Ordering of Transitions

In the context of transitions, the ordering by wavelength is based on the magnitude of the energy difference; transitions with smaller energy differences emit or absorb photons of longer wavelengths, whereas those with larger energy differences correspond to shorter wavelengths. Understanding this concept is key to arranging the transitions in order of decreasing wavelength.

Transcript

Please give Ace some feedback