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# Chapter Five: Many electron atom

الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 3
أستاذ المادة فؤاد عطية مجيد       04/11/2018 18:03:12
5.1 The Stern-Gerlach experiment and spin
Experiments in the early 1920s discovered a new aspect of nature and at the same time found the simplest quantum system in existence. In the Stern-Gerlach experiment, a beam of hot atoms is passed through a nonuniform magnetic field. This field would interact with the magnetic dipole moment of the atom, if any, and deflect it.

• This experiment discovered two surprising things. The atoms specifically, the unpaired outer electron did have a magnetic dipole moment. In effect, in addition to being charged, electrons acted like tiny bar magnets. They also, as it developed, have a tiny intrinsic amount of angular momentum, equal to . (This quantity is called spin, and all known elementary particles have nonzero spin.) Electrons are called spin-1/2 particles.
• The second surprising thing was how much the path of the electrons was deflected. If electrons were really bar magnets, they could be oriented in any direction. The component oriented along the magnetic field gradient (say the Z direction) would determine the force on the electron, and hence how much it would be deflected.
• If electrons were like ordinary magnets with random orientations, they would show a continuous distribution of paths. The photographic plate in the Stern-Gerlach experiment would have shown a continuous distribution of impact positions.
• What was observed was quite different. The electrons were deflected either up or down by a constant amount, in roughly equal numbers. Apparently, the Z component of the electron’s spin is quantized: it can take only one of two discrete values. We say that the spin is either up or down in the Z direction.
5.2 Quantum Numbers and Atomic Orbitals
From the solution of Schr?dinger equation for hydrogen atom in spherical coordinates, we obtained a set of mathematical equations, called wave functions, which describe the probability of finding electrons at certain energy levels within an atom.
A wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light).

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