I The first three energy levels of the fictitious element X...

I The first three energy levels of the fictitious element X are shown in Figure $\mathrm{P} 29.56$ a. What wavelengths are observed in the absorption spectrum of element $\mathrm{X} ?$ Give your answers in nm. b. State whether each of your wavelengths in part a corresponds to ultraviolet, visible, or infrared light. c. An electron with a speed of $1.4 \times 10^{6} \mathrm{m} / \mathrm{s}$ collides with an atom of element X. Shortly afterward, the atom emits a $1240 \mathrm{nm}$ photon. What was the electron's speed after the collision? Assume that, because the atom is so much more massive than the electron, the recoil of the atom is negligible.

I The first three energy levels of the fictitious element X are
shown in Figure $\mathrm{P} 29.56$
a. What wavelengths are observed in the absorption spectrum of element $\mathrm{X} ?$ Give your answers in nm.
b. State whether each of your wavelengths in part a corresponds to ultraviolet, visible, or infrared light.
c. An electron with a speed of $1.4 \times 10^{6} \mathrm{m} / \mathrm{s}$ collides with an atom of element X. Shortly afterward, the atom emits a $1240 \mathrm{nm}$ photon. What was the electron's speed after the collision? Assume that, because the atom is so much more massive than the electron, the recoil of the atom is negligible.

Key Concepts

Quantum Energy Levels

Atoms have discrete energy levels in which electrons can exist. Transitions between these levels occur when electrons absorb or emit energy, and these specific energy differences define the possible wavelengths of absorbed or emitted light.

Electron Transitions

When an electron moves between energy levels, it either absorbs or emits a photon whose energy corresponds exactly to the difference between the initial and final levels. These transitions are fundamental to understanding atomic absorption and emission spectra.

Absorption Spectrum

The absorption spectrum consists of the wavelengths at which an atom absorbs light as electrons are promoted from lower to higher energy levels. Each wavelength in the spectrum directly corresponds to a transition between specific quantized energy states.

Electromagnetic Spectrum Regions

Different regions of the electromagnetic spectrum—ultraviolet, visible, and infrared—are categorized based on wavelength. Identifying which region a particular wavelength falls into is important for analyzing the type of light involved in a transition.

Photon Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, according to the relation E = hc/?. This relationship is crucial for converting observed wavelengths into energy differences between atomic levels and for assessing the type of electromagnetic radiation emitted or absorbed.

Energy Conservation in Atomic Collisions

In collisions involving electrons and atoms, the principle of energy conservation governs the process. The kinetic energy lost by the electron is transferred to the atom, leading to electron excitation and subsequent photon emission. This concept is key to analyzing changes in electron speed after energy transfer events.

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