Why does the quantum mechanical description of many-electron atoms make it difficult to define a precise atomic radius?

Atoms and ions, at least within the quantum mechanical model do not have boundaries that are sharply defined at which the electron distribution becomes zero. When this occurs it can be very difficult to measure an atomic radius. The distance between the electrons in quantum mechanics is not set and would be problematic in determining the precise radius.

It indicates no change in temperature and the process of matter changing its state

Sorry i don’t know what to do