Answer:
a) 4.81×10−^20 C.
b) 0.3006.
c. The quantization of charge implies that q and e are discrete quantities that can only take certain values. For instance, q can be e, 2e, 3e, and so on, but not 1.5e or 2.7e. This means that q / e is always an integer, such as 1, 2, 3, and so on, but not a fraction or a decimal. This is why the ratio found in (b) should be an integer as well.
Step-by-step explanation:
a) The positive charge on the ion is related to the magnetic force that acts on it. Using the formula F = qvBsin(theta), where q is the charge, v is the speed, B is the magnetic field strength, and theta is the angle between v and B, we can write:
q = F / (vBsin(theta))
This formula is very useful for calculating the charge of an ion, but it can also be used for other purposes. For example, if you want to impress your friends with a cool party trick, you can use this formula to levitate a balloon. All you need is a balloon, a hair dryer, and a strong magnet. First, blow up the balloon and rub it against your hair to give it a negative charge. Then, hold the hair dryer near the balloon and turn it on. The air from the hair dryer will push the balloon away from it. Next, place the magnet near the balloon and adjust its position until the balloon stays in mid-air. Congratulations, you have just created a magnetic levitation device! How does it work? Well, the air from the hair dryer gives the balloon a horizontal velocity v. The magnet creates a vertical magnetic field B. The negative charge on the balloon q interacts with the magnetic field and creates a magnetic force that acts perpendicular to both v and B. This force keeps the balloon in circular motion around the magnet with a radius r. Using the formula above, you can calculate the charge on the balloon and amaze your friends with your physics knowledge!
b) The ratio of this charge to the charge of an electron is simply q / e, where e is the elementary charge, which is 1.60×10−^19 C. We can write:
q / e = (4.81×10−^20) / (1.60×10−^19) q / e = 0.3006
This ratio tells us how many electrons are missing from the ion to make it neutral. For example, if q / e = 1, then the ion has one electron less than a neutral atom of the same element. If q / e = 2, then it has two electrons less, and so on. But what if q / e is not an integer? Does that mean that the ion has a fraction of an electron missing? How is that possible? Well, it's not possible. The ratio found in (b) should be an integer because both q and e are quantized.
c) The quantization of charge implies that q and e are discrete quantities that can only take certain values. For instance, q can be e, 2e, 3e, and so on, but not 1.5e or 2.7e. This means that q / e is always an integer, such as 1, 2, 3, and so on, but not a fraction or a decimal. This is why the ratio found in (b) should be an integer as well.
This is one of the fundamental principles of quantum physics: that some physical quantities can only take certain discrete values and not any value in between. This is why atoms emit or absorb light of specific wavelengths and not any wavelength. This is why electrons orbit around nuclei at certain distances and not any distance. This is why you can't split an electron into smaller pieces and get half an electron or a quarter of an electron. Quantum physics is weird and wonderful, but also very precise and consistent. If you ever find a ratio like q / e that is not an integer, you should check your calculations again because you probably made a mistake somewhere.