Most rare earth metals are trivalent because they have three valence electrons in their outermost shell. This makes it energetically favorable for them to lose these three electrons to achieve a stable electron configuration. Additionally, the trivalent state allows rare earth metals to form stable compounds with other elements, making them useful in various industrial applications. **

No, smartphones are not possible without rare earth elements. These elements are essential components in the production of smartphones, as they are used in the manufacturing of various parts such as screens, batteries, and speakers. Without rare earth elements, smartphones would not be able to function as they do today, making them a crucial component in the production of these devices. **

Rare earth elements are primarily found in the electric car's permanent magnet motors, which are used in the vehicle's electric propulsion system. These elements, such as neodymium and dysprosium, are essential for the magnets that help generate the magnetic fields required for the motor to function efficiently. Additionally, rare earth elements can also be found in other components of the electric car, such as the battery, electronics, and sensors, although in smaller quantities compared to the motor. **

Analog devices generally do not require more rare earth elements than digital devices. Rare earth elements are used in the production of certain components in electronic devices, such as magnets and phosphors. While some analog devices may use rare earth elements in components like speakers or cathode ray tubes, digital devices also require rare earth elements for components like hard drives, batteries, and displays. Therefore, the use of rare earth elements is not inherently higher in analog devices compared to digital devices. **

For rare use, a laser printer may be more suitable than an inkjet printer. This is because laser printers use toner cartridges that do not dry out like ink cartridges, making them more reliable for occasional printing. Additionally, laser printers are known for their fast printing speeds and high-quality text output, which can be beneficial for occasional printing needs. Overall, a laser printer may be a more cost-effective and practical option for those who do not print frequently. **

Precious metals like gold, platinum, palladium, and rhodium are rare on Earth because they are not formed in abundance during the Earth's geological processes. These metals are typically formed during supernova explosions or neutron star collisions, which are rare events in the universe. Additionally, these metals are heavy and dense, causing them to sink deep into the Earth's core during its formation, making them less accessible on the Earth's surface. This rarity and difficulty in extraction contribute to their high value and desirability. **

For rare usage, I would recommend a basic inkjet printer. Inkjet printers are affordable and can handle occasional printing needs without the risk of the ink drying out. Look for a model with individual ink cartridges, so you only need to replace the color that runs out. Additionally, consider a printer with wireless connectivity for convenience and ease of use when you do need to print. **

Gold and platinum are considered rare metals, but they occur more frequently in the Earth's crust compared to rare earth metals. Gold and platinum are typically found in small concentrations in various geological formations, while rare earth metals are much less abundant and are often found in even smaller quantities. This scarcity of rare earth metals makes them more challenging and expensive to extract and process compared to gold and platinum. **