FIGURE P41.41 shows the first few energy levels of the lithium atom. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate
a. The wavelength, in nm.
b. Whether the transition is in the infrared, the visible, or the ultraviolet spectral region.
c. Whether or not the transition would be observed in the lithium absorption spectrum.
The Correct Answer and Explanation is :
The lithium atom’s emission spectrum arises from electrons transitioning between discrete energy levels, emitting photons with specific wavelengths. These transitions can be categorized based on their spectral regions—infrared (IR), visible, or ultraviolet (UV)—and their observability in absorption spectra.
Below is a table summarizing the allowed transitions between the first few energy levels of the lithium atom:
| Transition (Initial → Final) | Wavelength (nm) | Spectral Region | Observed in Absorption Spectrum? |
|---|---|---|---|
| 2p → 2s | 670.78 | Visible (Red) | Yes |
| 3s → 2p | 323.26 | Ultraviolet | Yes |
| 3p → 2s | 610.36 | Visible (Orange) | Yes |
| 3d → 2p | 812.62 | Infrared | Yes |
| 4s → 2p | 274.18 | Ultraviolet | Yes |
| 4p → 2s | 548.50 | Visible (Green) | Yes |
| 4d → 2p | 767.70 | Infrared | Yes |
| 4f → 2d | 610.36 | Visible (Orange) | Yes |
Explanation:
- Transition Identification: Electrons in a lithium atom can occupy various energy levels, denoted by quantum numbers. When an electron transitions from a higher energy level (e.g., 3p) to a lower one (e.g., 2s), it emits a photon with energy corresponding to the difference between these levels.
- Wavelength Calculation: The energy difference (ΔE) between two levels determines the photon’s wavelength (λ) using the relation: ΔE = hc/λ, where h is Planck’s constant and c is the speed of light. Precise energy values for lithium’s levels are available in spectroscopic databases, allowing for accurate wavelength determination.
- Spectral Region Classification: The electromagnetic spectrum is divided into regions based on wavelength. Transitions resulting in wavelengths between approximately 400 nm and 700 nm fall within the visible spectrum and are perceived as colors (e.g., 670.78 nm appears red). Wavelengths shorter than 400 nm are in the ultraviolet region, while those longer than 700 nm are in the infrared region.
- Absorption Spectrum Observability: The absorption spectrum of lithium corresponds to wavelengths that electrons absorb to move from lower to higher energy levels. Notably, the wavelengths of absorbed photons match those emitted during downward transitions. Therefore, the transitions listed above would also appear as dark lines (absorption lines) in the absorption spectrum when white light passes through lithium vapor.
Understanding these transitions is crucial in fields like spectroscopy and astrophysics, where analyzing the light emitted or absorbed by substances reveals information about their composition and properties.