Final answer:
The question asks to rank the period of motion of particles A to D, which requires knowledge of the particles' specific motion in physics. However, based on the information provided, each particle's period within a cyclotron is constant, so additional context is needed. For simple harmonic motion, a particle travels a distance of 4A in one time period.
Step-by-step explanation:
The original question is asking to rank the period of the motion of particles A to D from largest to smallest. This question is related to a concept in physics about periodic motion and simple harmonic motion. The period of the motion is the time it takes to complete one full cycle of that motion. From the provided description, each particle in a cyclotron completes a semicircular orbit within a time T/2, and then the polarity is switched, allowing the particle to continue its path to the subsequent semicircular orbit. This process allows particles to gain kinetic energy and move to orbits of slightly larger radii. The period of each particle's motion would technically remain constant throughout the process because each completes its path in a time T. However, if the question is regarding periods of motion within different dees (D1, D2, etc.), such information is insufficient to rank them without additional details on the specific scenario of particles A to D.
For a simple harmonic motion, the particle will travel a distance of 4 times the amplitude A in one time period. This is because it moves from the mean position to one extreme, back through the mean to the other extreme, and returns to the mean position, accounting for a total of 4A.
The particles' movement direction in different mediums, such as up and down in a wave traveling through a medium or right and left in a vacuum, doesn't provide direct information to rank the period of motion from largest to smallest for particles A to D without further clarification on the context in which these particles exist.