## 21.1 Electromagnetic Wave This section introduces the concept of electromagnetic (EM) waves, their properties, the electromagnetic spectrum, and the foundational principles of Planck's Quantum Theory, which describes how energy is emitted and absorbed at the atomic level. ## Electromagnetic Waves - **Origin:** First proposed by James Clerk Maxwell in 1864, EM waves are generated by **accelerated electric charges**. - **Composition:** They consist of linked, oscillating **electric (E) and magnetic (B) fields** that sustain each other. - **Propagation:** - The E and B fields are **mutually perpendicular** and also perpendicular to the direction of wave propagation. - The direction of travel is given by the vector product $\mathbf{E} \times \mathbf{B}$. - They can travel through a vacuum or a medium. - **Speed:** The speed of an EM wave in a vacuum is the speed of light, approximately $c \approx 3 \times 10^{8} \mathrm{m} \mathrm{s}^{-1}$. ## The Electromagnetic Spectrum The spectrum encompasses all types of electromagnetic radiation, categorized by wavelength or frequency. Examples include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The **visible light spectrum** for humans lies between wavelengths of approximately **390 nm (Violet)** and **750 nm (Red)**. ## Planck's Quantum Theory Proposed by Max Planck in 1900, this theory marked the beginning of quantum physics. Its main postulates are: 1. **Quantization of Energy:** Atoms and molecules can only emit or absorb energy in discrete, specific amounts. The energy of the radiation is given by the formula: $$E = n h f$$ - $E$ is the energy of the radiation. - $n$ is the **quantum number**, an integer ($1, 2, 3, \ldots$). - $h$ is **Planck's constant**, $h = 6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$. - $f$ is the **frequency** of the radiation. 2. **Quantum:** The smallest, indivisible packet of energy that can be emitted or absorbed in the form of electromagnetic radiation is called a **quantum** (plural: quanta). Atoms jump between allowed energy states (quantum states) by absorbing or emitting a quantum of energy. ## Possible Questions and Answers **Q:** What is the frequency of a photon whose energy is 66.3 eV? **A:** First, convert the energy to Joules: $$E = 66.3 \mathrm{eV} \times (1.6 \times 10^{-19} \mathrm{J/eV}) = 1.06 \times 10^{-17} \mathrm{J}$$ Then, using the formula $E = hf$, the frequency is calculated as: $$f = \frac{E}{h} = \frac{1.06 \times 10^{-17}}{6.626 \times 10^{-34}} = 1.6 \times 10^{16} \mathrm{Hz}$$ --- **Q:** (Assignment 21.1) What will be the photon energy for a wavelength of 5000 angstroms, if the energy of a photon corresponding to a wavelength of 7000 angstroms is $4.23 \times 10^{-19}$ J? **A:** Energy is inversely proportional to wavelength ($E = hc/\lambda$, so $E \propto 1/\lambda$). We can set up a ratio: $E_2/E_1 = \lambda_1/\lambda_2$. $$E_2 = E_1 \times \frac{\lambda_1}{\lambda_2} = (4.23 \times 10^{-19} \mathrm{J}) \times \frac{7000 \text{ angstroms}}{5000 \text{ angstroms}} = 5.922 \times 10^{-19} \mathrm{J}$$ | Key Formula/Constant | Description | Value | | :--- | :--- | :--- | | $E = nhf$ | Energy of quantized radiation | $n = 1, 2, 3, \ldots$ | | $h$ | Planck's constant | $6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$ | | $c$ | Speed of light in vacuum | $\approx 3 \times 10^{8} \mathrm{m} \mathrm{s}^{-1}$ |