Energy (frequency) and Time are related via the Fourier Transform of the Wave Function. A quantum state has to hang around for a while in order to have a precise energy value. In other words, it takes time to define one whole cycle of a frequency. But it takes less time to define one whole cycle of a frequency for higher frequencies than for lower frequencies. My question: Suppose that we have two sources of (hypothetical) particles, one source is known to be of higher energy than the other source. Assume also that our hypothetical particles both decay in the same amount of time. Would the particles from the high energy source have more precise (smaller relative standard deviation) energy than the particles from the lower energy source? Does it take less time to precisely define energy for higher energy particles than for lower energy particles? Thanks in advance.