Match the theoretical motion of particles with their associated phases Match the items in the left column to the items in the right column. 1. oscillation about a fixed point square gas square solid square liquid 2. translation, vibration rotation 3. rotation and vibration

To match the theoretical motion of particles with their associated phases, consider the typical behavior of particles in each state of matter:<br /><br />1. **Oscillation about a fixed point** <br /> - This is characteristic of particles in a **solid**. In solids, particles are closely packed and can only oscillate around their fixed positions.<br /><br />2. **Translation, vibration, rotation** <br /> - These motions are typical of particles in a **gas**. Gas particles have enough energy to move freely and independently, allowing for translation (movement from one place to another), as well as vibration and rotation.<br /><br />3. **Rotation and vibration** <br /> - These motions are characteristic of particles in a **liquid**. In liquids, particles are close together but not in fixed positions, allowing them to rotate and vibrate while still being able to flow past one another.<br /><br />So, the matches are:<br />- Oscillation about a fixed point: **solid**<br />- Translation, vibration, rotation: **gas**<br />- Rotation and vibration: **liquid**