Quantum numbers fourth

Nuclear magnetic resctnance involves the transitions between energy levels of the fourth quantum number, the spin quantum number, and only certain nuclei whose spin is not zero can be studied by this technique. Atoms having both an even number of protons and neutrons have a zero spin for example, carbon 12, oxygen 16 and silicon 28. 

Dirac showed in 1928 dial a fourth quantum number associated with intrinsic angidar momentum appears in a relativistic treatment of the free electron, it is customary to treat spin heiiristically. In general, the wavefimction of an electron is written as the product of the usual spatial part (which corresponds to a solution of the non-relativistic Sclnodinger equation and involves oidy the Cartesian coordinates of the particle) and a spin part a, where a is either a or p. A connnon shorthand notation is often used, whereby... 

The fourth quantum number is called the spin angular momentum quantum number for historical reasons. In relativistic (four-dimensional) quantum mechanics this quantum number is associated with the property of symmetry of the wave function and it can take on one of two values designated as -t-i and — j, or simply a and All electrons in atoms can be described by means of these four quantum numbers and, as first enumerated by W. Pauli in his Exclusion Principle (1926), each electron in an atom must have a unique set of the four quantum numbers. 

For reasons we will discuss later, a fourth quantum number is required to completely describe a specific electron in a multielectron atom. The fourth quantum number is given the symbol ms. Each electron in an atom has a set of four quantum numbers n, l, mi, and ms. We will now discuss the quantum numbers of electrons as they are used in atoms beyond hydrogen. 

The fourth quantum number, ms> is associated with electron spin. An electron has magnetic properties that correspond to those of a charged particle spinning on its axis. Either of two spins is possible, clockwise or counterclockwise (Figure 6.5). 

These days students are presented with the four quantum number description of electrons in many-electron atoms as though these quantum numbers somehow drop out of quantum mechanics in a seamless manner. In fact, they do not and furthermore they emerged, one at a time, beginning with Bohr s use of just one quantum number and culminating with Pauli s introduction of the fourth quantum number and his associated Exclusion Principle. 

Figure 6. Wolfgang Pauli s discovery of the exclusion principle led to his development of a fourth quantum number to describe the electron. At the time, it was known that each successive electron shell in an atom could contain % 8, 18. .. 2nz electrons (where n is the shell number), and Pauli s fourth number made it possible to explain this. When an electron s first quantum number is one, the second and third must be zero, leaving two possibilities for the fourth number Thus the first shell can contain only two electrons. At = 2, there are four possible combinations of the second and third numbers, each of which has two possible fourth numbers. Thus the second shell closes when it contains eight electrons.

As many textbooks correctly report, the number of electrons that can be accommodated into any electron shell coincides with the range of values for the three quantum numbers that characterize the solutions to the Schrodinger equation for the hydrogen atom and the fourth quantum number as first postulated by Pauli. 

For example, if the first quantum number is 3 the second quantum number can take values of 2, 1, or 0. Each of these values of will generate a number of possible values of mt and each of these values will be multiplied by a factor of two since the fourth quantum number can adopt values of 1/2 or -1/2. As a result there will be a total of 2n2 or 18 electrons in the third shell. This scheme thus explains why there will be a maximum total of 2, 8, 18, 32, etc., electrons in successive shells as one moves further away from the nucleus. 

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

Ans. The letter s represents the fourth quantum number—the spin quantum number. It also represents the subshell with an / value of 0. 

The fourth quantum number is the spin quantum number (ms) and indicates the direction the electron is spinning. There are only two possible values for ms, + V2 and —V2. When two electrons are to occupy the same orbital, then one must have an ms = +V2 and the other electron must have an ms = -V2. These are spin-paired electrons. 

In order to understand how electrons of many-electron atoms arrange themselves into the available orbitals it is necessary to define a fourth quantum number ... 

Pauli proposed the use of a fourth quantum number, which could have two values, thereby explaining why it is that electrons with identical energies behave differently in a strong magnetic field. If it is assumed that no two electrons in an atom may occupy the same atomic state, meaning that no two electrons can have the same four quantum numbers, then there might be two, but no more than two, 5 electrons for each principal quantum number. Six different... 

In late fall 1925, the Dutch physicists G. Uhlenbeck and Samuel Goudsmit gave a physical interpretation to Pauli s postulate of a fourth quantum number. The electron, they proposed, may spin in one of two directions. In a given atom, a pair of electrons having three identical quantum-number values must have their spin axes oriented in opposite directions, and if paired oppositely in a single orbital, they neutralize each other magnetically. 22... 

The fourth quantum number, the spin quantum number (m), indicates the direction the electron is spinning. There are only two possible values for ms, + / and —A. 

As for the third and fourth quantum numbers, in agreement with what is generally mentioned in textbooks on chemistry, such as, for instance, Greenwood and Earnshaw (1997) we may say that ... 

Orbitals have a variety of different possible shapes. Therefore, scientists use three quantum numbers to describe an atomic orbital. One quantum number, n, describes an orbital s energy level and size. A second quantum number, I, describes an orbital s shape. A third quantum number, mi, describes an orbital s orientation in space. These three quantum numbers are described further below. The Concept Organizer that follows afterward summarizes this information. (In section 3.3, you will learn about a fourth quantum number, mg, which is used to describe the electron inside an orbital.)... 

As you learned from the previous section, three quantum numbers—n, 1, and mi—describe the energy, size, shape, and spatial orientation of an orbital. A fourth quantum number describes a property of the electron that results from its particle-like nature. Experimental evidence suggests that electrons spin about their axes as they move throughout the volume of their atoms. Like a tiny top, an electron can spin in one of two directions, each direction generating a magnetic field. The spin quantum number (mj specifies the direction in which the electron is spinning. This quantum number has only two possible values or —... 

What is the fourth quantum number, and why does it have only two possible values ... 

The principal quantum number, n, is related to the size of the orbital. A second quantum number, the angular momentum quantum number, I, is used to represent different shapes of orbital. The orientation of any non-spherical orbital is indicated by a third quantum number, the magnetic quantum number, m. A fourth quantum number, the spin quantum number, s, indicates the spin of an electron within an orbital. 

When dealing with atoms possessing more than one electron it is necessary to introduce a fourth quantum number s, the spin quantum number. However, to take into account the intrinsic energy of an electron, the value of 5 is taken to be A. Essentially the intrinsic energy of the electron may interact in a quantized manner with that associated with the angular momentum represented by /, such that the only permitted interactions are l + s and / - s. For atoms possessing more than one electron it is necessary to specify the values of s with respect to an applied magnetic field these are expressed as values of ra of + A or - A. 

In addition, a relativistic treatment of the electron introduces a fourth quantum number, the spin, m, with ms = j. This is because every electron has associated with it a magnetic moment which it quantized in one of two possible orientations parallel with or opposite to an applied magnetic field. 

According to quantum mechanics, an electron has two spin states, represented by the arrows t and 1 or the Greek letters a and (3. We can think of an electron as being able to spin counterclockwise at a certain rate (the T state) or clockwise at exactly the same rate (the i state). These two spin states are distinguished by a fourth quantum number, the spin magnetic quantum number, ms. This quantum number can have only two values Tj indicates an t electron and —j indicates a l electron (Fig. f.30). Box 1.1 describes how spin explains the results of an important experiment. 

A FIGURE 5.15 Electrons behave in some respects as if they were tiny charged spheres spinning around an axis. This spin (blue arrow) gives rise to a tiny magnetic field (green arrow) and to a fourth quantum number, ms, which can have a value of either +1/2 or—1/2. 

The three quantum numbers n, l, and wi/ discussed in Section 5.7 define the energy, shape, and spatial orientation of orbitals, but they don t quite tell the whole story. When the line spectra of many multielectron atoms are studied in detail, it turns out that some lines actually occur as very closely spaced pairs. (You can see this pairing if you look closely at the visible spectrum of sodium in Figure 5.6.) Thus, there are more energy levels than simple quantum mechanics predicts, and a fourth quantum number is required. Denoted ms, this fourth quantum number is related to a property called electron spin. 

Think about the consequences of the Pauli exclusion principle. Electrons that occupy the same orbital have the same three quantum numbers, n, l, and tri[. But if they have the same values for n, l, and wz/, they must have different values for the fourth quantum number either ms = +1/2 or ms = —1/2. Thus, an orbital can hold only two electrons, which must have opposite spins. An atom with x number of electrons therefore has at least x /2 occupied orbitals (though it might have more if some of its orbitals are only half-filled). 

For atoms with more than one electron, we must take account of a fourth quantum number, ms, the electron spin quantum number, which has only two values, ms = 1/2. An electron has a magnetic moment which can be rationalized by imagining that electrons spin about an... 

The fourth quantum number is the spin number. Electrons are said to have either a +lA spin or a -A spin, which we might think of as clockwise and counterclockwise, respectively. Within any orbital, the first electron is said to have a positive spin, whereas the second electron has a negative spin. 

Each orbital can contain a maximum of two electrons, and these must have opposite spins. This is a result of the Pauli exclusion principle, which states that no two electrons can have all four quantum numbers the same. Because two electrons in the same orbital must have three of the quantum numbers the same, the fourth quantum number (the spin quantum number) must be different. 

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