Fig 7.1 The SG experiment
There must be questions raised why choose Silver atom not any other? But first before getting answer to that question one should know what exactly is spin. Spin in quantum mechanics is not something we physically describe things. Spin is just the two state of any electron which is in its purest state. Purest state means here that the probability of electron to be in a specific position is 100%. The atom can be influenced by various experiments to be in its purest state. The SG experiment is one of the experiment in understanding electron's spin behavior. Spin has two states as +1/2 and -1/2 regarded as up and down positions respectively. Spin states are not fixed meaning it is not already in either of the two positions but they just move to one of the states quickly after we start observing one of the electron spins. Its called quantum entanglement in which one state influences other very quickly. This superposition of electrons and quantum entanglement idea is used in supercomputer for sharing qubits (0 or 1) information very quickly through various algorithms. The spin in an atom is from its nucleus which is a sum of spins from protons and nucleus. The other spin is from electrons. This spin creates a tiny magnetic field and magnetic moment which is going to be very important in the SG experiment.
So, coming back to the first question raised of choosing silver atom. The silver atom is made up of nucleus and total 47 electrons where 46 out of 47 electrons can be visualized as forming a spherically symmetrical electron cloud as shown in the fig 7.1. According to Pauli's exclusion principle, in one orbital, two electrons cannot exist with same spin state. According to Pauli's exclusion principle and the following filling of orbital configuration of electrons in silver atom: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹⁰, here we see that the 5s orbital has one unpaired electron which is responsible for only spin-intrinsic angular momentum and not the orbital angular momentum because its zero for s-orbitals. The single 47th electron mass which is attached to the nucleus is very very small (~2*10^5) times smaller than the nucleus mass. So, according to the relation: μ (magnetic moment) ∝ (q/m)×(angular momentum), the magnetic moment is very very small from nucleus and the almost all the magnetic moment is just from the 47th single electron. There will not be any other external disturbance to influence the electron from not going to its spin states which is also called as quantized state because it is fixed and so μ (magnetic moment of the atom) ∝ S (electron spin). The effect of nucleus spin in electron spin is used in atomic clock. Here, in this experiment we just ignored the effect of nucleus spin. So, overall this is the reason for choosing silver atom here in the experiment.
The z component of force experienced by the atom is : Fz=∂(μ⋅B)/ ∂z = μz ∂Bz/∂z. In fig 7.1, μz > 0 ( Sz < 0) then atom experiences upward force, while μz < 0 ( Sz > 0) atom experiences downward force. The electrons negative changes sign inverses the direction and signs of μz and Sz. The beam is expected to split according to the values of μz. The SG experiment measures the z component of μ or z component of S up to a proportionality factor.
The atoms in the oven are randomly oriented; there is no preferred direction for the orientation of μ. If the electrons were like a classical spinning object, we would expect all values of μz to be realized between | μ | and | -μ |. This would lead us to expect a continuous bundle of beams coming out of the SG experiment as in fig 7.1 to be spread more or less evenly over the expected range. In the SG experiment, the electrons are passed through the inhomogeneous magnetic field which is essential for getting the observational result of spin. If we use homogeneous magnetic field then the electrons would just rotate and there will be no net force on electron spin due to homogeneous magnetic field and we will not be able to see the deflection in upward and downward direction of electrons due to spin. The inhomogeneous creates a varying strength magnetic field which forces the electrons to go into upward and downward direction according to its spin. The inhomogeneous magnetic field creates this net force on the electron which is essential because it converts the abstract quantum property (spin) into a spatial separation of the atom beam, which can be observed directly on the screen.
But the actual experiment showed that there are only 2 spots observed corresponding to one "up" and one "down" orientation. The SG apparatus splits the original silver beam from the oven into 2 distinct components (space quantized). The values of Sz are: Sz=±ℏ/2 where ℏ is Planck's constant = 1.0546 * 10^-27 erg-s = 6.5822 * 10^-16 eV-s.
In this experiment, we just setup one single SG apparatus which just quantizes the spin in only one specific direction ( z direction). In the next chapter, we are going to see what happens if the spin is quantized in multiple directions ( x, y, z) by setting multiple SG apparatus in parallel in multiple directions and what will be the classical expectation and experimental observation from this experiment.
Great insights Krish
ReplyDeleteThanks Ved!
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