No, polarizability and polarity are not the same. Polarity refers to the distribution of electric charge in a molecule, which results in a molecule having a positive and negative end. Polarizability, on the other hand, refers to the ability of a molecule to be distorted by an external electric field. In other words, polarizability is a measure of how easily the electron cloud in a molecule can be distorted, while polarity is a measure of the overall charge distribution within a molecule. **

The polarizability of a wave refers to its ability to induce an electric dipole moment in a material. When a wave interacts with a material, it can cause the charges within the material to separate, creating an electric dipole moment. The extent to which this occurs is determined by the polarizability of the wave. In other words, the polarizability measures how easily a wave can cause the charges in a material to rearrange in response to its presence. **

The atomic radius of an atom is dependent on the number of electron shells it has, as well as the effective nuclear charge experienced by the outermost electrons. As the number of electron shells increases, the atomic radius also increases. The electronic polarizability of an atom refers to its ability to distort its electron cloud in the presence of an external electric field. This property is related to the ease with which the electron cloud can be distorted, which in turn is influenced by the size of the atom and the distribution of its electrons. **

Yes, underhand serves are allowed in professional tennis matches. While they are less common and often seen as unconventional, there is no rule against using an underhand serve. In fact, some players have used underhand serves to surprise their opponents and gain an advantage. However, underhand serves are generally considered less powerful and can be riskier to use in high-stakes matches. **

The volleyball serve may not go over the net due to various reasons such as improper technique, lack of power, or hitting the ball at the wrong angle. Serving requires a combination of timing, strength, and precision to ensure the ball clears the net and lands in the opponent's court. Players need to practice and refine their serving skills to consistently execute successful serves. **

No, in a professional tennis match, the serve must be executed from above the player's head. The rules of tennis dictate that the serve must be hit from behind the baseline and above the level of the server's waist. Serving from below the waist would be considered a fault and the server would have to retake the serve. **

Yes, the ball can touch the net during a serve in volleyball as long as it goes over the net and into the opponent's court. However, if the ball hits the net and does not go over, it is considered a fault and the serving team loses the point. Players often aim to serve the ball over the net without touching it, but a slight touch of the net is allowed as long as the ball continues into the opponent's court. **

One can train footwork at home by setting up a small agility ladder or using tape to create a ladder pattern on the floor. Practice different footwork drills such as high knees, lateral shuffles, and quick steps through the ladder. Additionally, one can incorporate exercises like jump rope, box jumps, and speed ladder drills to improve footwork and agility. It's also important to focus on proper form and technique while performing these drills to maximize the effectiveness of the training. **