## **21.9 DISCRETE ENERGY LEVELS IN AN ATOM AND ITS SPECTRA** The electrons orbiting an atom are restricted to specific, allowed orbits, also known as shells. Each orbit corresponds to a discrete energy level for the atom (e.g., $E_{1}, E_{2}, E_{3}, \dots$). Electrons can only transition between these levels by absorbing or emitting a precise amount of energy. ### **Electron Transitions** - ***Excitation:*** An electron moves from a lower energy level to a higher one by **absorbing** energy. - ***De-excitation:*** An electron moves from a higher energy level to a lower one by **releasing** energy. The energy is absorbed or emitted as electromagnetic radiation (a photon) with a specific frequency, $f$. The relationship between the energy difference of the levels and the photon's frequency is given by Bohr's second postulate: $$h f = E_{n} - E_{p}$$ Where: - $h$ is Planck's constant - $f$ is the frequency of the photon - $E_{n}$ is the energy of the higher state - $E_{p}$ is the energy of the lower state ### **Atomic Spectra** When the light emitted or transmitted by a substance is passed through a prism or diffraction grating, it is separated into its constituent wavelengths, forming a **spectrum**. Because atomic energy levels are discrete, atoms produce a **line spectrum**, which consists of a set of distinct lines rather than a continuous band of colours. Each element has a unique line spectrum, which acts as its "fingerprint". ### **Types of Line Spectra** | Feature | **Emission Spectrum** | **Absorption Spectrum** | |---------------------|-------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------| | **Appearance** | A series of separate **bright lines** on a dark background. | A series of separate **dark lines** on a continuous, coloured background. | | **Formation** | Produced when excited atoms in a hot, low-pressure gas or vapour **emit photons** of specific frequencies as they de-excite. | Produced when white light passes through a cool gas or vapour. Atoms **absorb photons** of specific frequencies, causing excitation. | | **Example** | A neon sign glowing with its characteristic red colour. | Analyzing the light from a star passing through its cooler outer atmosphere to determine its composition. | | **Visual Example** | | | *Figure 21.13: Comparison of (a) the H-emission spectrum and (b) the H-absorption spectrum. The lines appear at the same wavelengths.* ### **Spectral Series of Hydrogen** The hydrogen spectrum consists of several series of lines named after their discoverers. These series occur when electrons transition from higher orbits ($n$) to a specific lower orbit ($p$): 1. **Lyman Series:** Transitions to $p=1$ (Ultraviolet region). 2. **Balmer Series:** Transitions to $p=2$ (Visible region). 3. **Paschen Series:** Transitions to $p=3$ (Infrared region). 4. **Brackett Series:** Transitions to $p=4$ (Infrared region). 5. **Pfund Series:** Transitions to $p=5$ (Infrared region). ### **Energy States and Potentials** - **Ground State:** The lowest energy state of an atom ($n=1$). - **Excited State:** Any state with energy higher than the ground state ($n > 1$). - **Excitation Potential:** The potential difference required to provide an electron with enough energy to jump from the ground state to an excited state. | **Key Formula** | **Description** | |-----------------------------------------------|--------------------------------------------------------------------------------| | $h f = E_{n} - E_{p}$ | Relates the frequency ($f$) of an emitted/absorbed photon to the energy difference between two atomic levels ($E_n$ and $E_p$). |