Therefore their momentum perpendicular to the beam direction becomes increasingly less defined. The more they limit the diameter of a light beam, the more the position of the photons becomes exactly defined perpendicular to the beam direction. With light-based analytical instruments the designers of the optics have to struggle with the uncertainty principle. A piece of neutron star the size of a sugar cube therefore weighs several hundred million tons. However, on neutron stars – these are burnt out stars with a remaining mass in the order of magnitude of our sun, but with a diameter of only approximately 30 kilometers – the force of gravity is so strong that the electrons are squeezed into the nucleus. This is not possible under normal conditions on Earth, thus explaining the stability of the atoms. This amount of energy would need to be applied to the atom in order to squeeze it down. If the atom was to be squeezed down to one tenth of its original size this would mean that the momentum of the electron would increase ten-fold and its energy would increase approximately one-hundred-fold. The absolute square value of the wave amplitude at each position gives the probability of finding the electron in this position. These standing waves are called orbitals. Instead they form standing waves around the atomic nucleus. Electrons can therefore have no defined orbits.
![uncertainty principle uncertainty principle](https://i.ytimg.com/vi/bHNazVPtK1s/maxresdefault.jpg)
It follows that the uncertainty of the speed of the electrons is in the order of magnitude of 1000 kilometers per second. This has many consequences: Atoms are approximately 0.1 nanometers in size, which means that their electrons are limited to this space.
![uncertainty principle uncertainty principle](https://image1.slideserve.com/3014486/slide14-l.jpg)
We can summarize this as follows: If the position of a quantum object is exactly defined its momentum and speed must be undetermined and vice versa. For measurements this means that we measure very different momentum values despite identical preparation of the particles.
![uncertainty principle uncertainty principle](https://hips.hearstapps.com/hmg-prod.s3.amazonaws.com/images/heisenberg-1580845638.jpg)
Consequently, the momentum – which is inversely proportional to the wavelength – has no sharply defined value but a wide distribution. A narrow wave packet therefore consists of many waves with different wavelengths.