It's completely acceptable to work out one body part a day. In fact, most fitness professionals will tell you not to work the same muscle group on consecutive days, particularly when it comes to strength training. Your muscles need time to recover, so working one body part a day falls within this guideline. You should, however, realize that it's next to impossible to work the back or chest without working the arms; or the quads and hams without working the glutes and calves. This is important to keep in mind when establishing a workout routine.
Strength training forces the muscles to contract under resistance, which leads to damage within the muscular fibers. Like any other trauma, the body responds by rebuilding the damaged tissue. Instead of regenerating it as before, however, the body thickens these fibers to help meet the demands of the increased workload, thereby increasing both strength and mass.
The thickening of muscle fibers doesn't happen overnight. It takes time to complete this process of muscle recovery. The length of time often varies based on the size of the muscle. As a general rule, small muscles take less time to recover than larger ones. Biceps, triceps and calves take about two days to recover, whereas the chest, back and thighs are more inclined to take three days.
Muscle recovery is one of the main reasons why most people subscribe to the two-way or three-way split. The two-way split usually works the upper body on the first day and then the lower body on the second day, with the third day reserved for rest. The three-way split works upper body with pushing exercises on day one, the lower body on day two and the upper body with pulling exercises on day three. The fourth day is reserved for rest. Pushing exercises tend to focus on the chest, shoulders and triceps, while pulling exercises focus more on the back and biceps.
If your plan is to focus on one body part a day, you're looking at more of a four-way split: chest, back, legs and arms. The only difference is that you're devoting a single day to the arms. In this situation, you may want to rearrange your routine to upper body pushing exercise on the first day, upper body pulling exercises on the second day, lower body on the third day and arms on the fourth day, leaving the fifth day for rest. This should give your muscles enough time to recover between workouts.