Which of the following is not the possible path of cathode rays ejecting from the surface of cathode — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Fundamental Principle of Cathode Ray Emission Cathode rays, which consist of high-energy streams of electrons, are ejected from the negative electrode (the cathode) under high voltage in a gaseous discharge tube. A key physical property of cathode rays is that **they are always emitted normally (perpendicularly) to the surface of the cathode**. This perpendicular emission occurs because: 1. The metal cathode behaves as an equipotential surface. 2. The electric field lines ($\vec{E}$), which exert the electrostatic force that accelerates the electrons outward, must always be perpendicular to this equipotential surface at every point: $$\vec{E} \perp \text{Surface of Cathode}$$ Consequently, the initial direction and path of the ejected cathode rays are determined solely by the geometry (shape) of the cathode's surface. --- ### Step 2 - Analysis of Cathode Geometries and Resulting Paths 1. **Flat (Plane) Cathode:** All local normals are parallel. Rays emerge as a parallel straight beam. 2. **Convex Cathode:** Surface normals diverge outward → Diverging beam. 3. **Concave Cathode:** Surface normals converge toward a focal region → Converging beam. --- ### Step 3 - Systematic Analysis of the Options and Diagrams * **Option (A) Figure (a):** Straight, parallel rays from a flat cathode — physically **possible** and correct. Not the answer. * **Option (B) Figure (b):** Diverging rays from a convex cathode — physically **possible** and correct. Not the answer. * **Option (C) Figure (c):** Converging rays from a concave cathode — physically **possible** and correct. Not the answer. * **Option (D) Figure (d):** Curved, non-perpendicular rays from a flat cathode — In the absence of an external deflecting field, there is no force capable of causing electrons to eject at oblique angles or to spontaneously curve. This path is **physically impossible**. $$\text{Correct Option: } \boxed{\text{D}}$$