Final answer:
The uncertainty principle entails a non-zero probability of finding the 1s orbital of a hydrogen atom empty even at zero Kelvin, though this is extremely rare. To define this precisely would require quantum mechanical calculations, but the probability cloud suggests the electron is usually within the 1s orbital.
Step-by-step explanation:
The time-energy uncertainty principle implies that the precise energy (and therefore the exact state) of a particle cannot be known at all times. For the 1s orbital of a hydrogen atom, the uncertainty principle suggests there's always a non-zero probability of finding the orbital empty even at zero Kelvin, as the electron's exact position cannot be pinpointed to be within that orbital at all times.
In classical terms, an electron might spontaneously jump to a higher energy level due to fluctuations allowed by the uncertainty principle, even without external energy input, though this occurrence would be extremely rare.
However, quantum mechanics tells us that the electron in the ground state of a hydrogen atom has a certain probability cloud, indicating where the electron is likely to be found upon measurement. The probability of the electron being found at any specific point, including outside the 1s orbital, is given by the squared magnitude of the wave function for that point.
Nonetheless, specific calculations must take into account complex quantum mechanical principles and the actual wave function of the electron. The estimation of the actual probability for the 1s electron to be outside the Bohr radius or to find the 1s orbital empty would require solving the Schrödinger equation for the hydrogen atom.
General chemistry knowledge and the features of the probability cloud indicate that the electron is most likely to be found within the 1s orbital, and it is exceptionally unlikely to be found completely absent from the orbital for any measurable period.