Quantum number, magnetic principal

The valence electron for the cesium atom is in the 6s orbital. In assigning quantum numbers, n = principal energy level = 6. The quantum number l represents the angular momentum (type of orbital) with s orbitals = 0, p orbitals = 1, d orbitals = 2, and so forth. In this case, l = 0. The quantum number m is known as the magnetic quantum number and describes the orientation of the orbital in space. For, v orbitals (as in this case), mt always equals 0. For p orbitals, mt can take on the values of -1, 0, and +1. For d orbitals, can take on the values -2, -1, 0, +1, and +2. The quantum number ms is known as the electron spin quantum number and can take only two values, +1/2 and -1/2, depending on the spin of the electron. 

According to quantum mechanics, electrons in atoms occupy the allowed energy levels of atomic orbitals that are described by four quantum numbers the principal, the azimuthal, the magnetic, and the spin quantum numbers. The orbitals are usually expressed by the principal quantum numbers 1, 2, 3, —increasing from the lowest level, and the azimuthal quantum numbers conventionally eiqiressed by s (sharp), p (principal), d (diffuse), f (fundamental), — in order. For instance, the atom of oxygen with 8 electrons is described by (Is) (2s) (2p), where the superscript indicates the munber of electrons occupying the orbitals, as shown in Fig. 2-1. 

The quantum mechanical model proposed in 1926 by Erwin Schrodinger describes an atom by a mathematical equation similar to that used to describe wave motion. The behavior of each electron in an atom is characterized by a wave function, or orbital, the square of which defines the probability of finding the electron in a given volume of space. Each wave function has a set of three variables, called quantum numbers. The principal quantum number n defines the size of the orbital the angular-momentum quantum number l defines the shape of the orbital and the magnetic quantum number mj defines the spatial orientation of the orbital. In a hydrogen atom, which contains only one electron, the... 

The resulting RPAE equation for the photoionization amplitude Dn from an initial state i i into a final state V2, (v is the total set of quantum numbers that characterize a single-electron state the principal quantum number n, orbital quantum number /, magnetic quantum number mi, and the z projection of the electron spin sz) is given by [55]... 

In standard introductory text books, the quantum mechanics of the hydrogen atom is usually discussed in spherical coordinates. In the spherical description, neglecting the electron spin, the hydrogen states are classified with the help of three quantum numbers, the principal quantum number n, the angular quantum number I and the magnetic quantum number m. The hydrogen wave functions are given by... 

Which of the following is NOT a possible set of quantum number values for the nitrogen atom, in the order of principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number ... 

Each electron in an atom is characterized by four different quantum numbers. The distribution of an electron in space— its atomic orbital—is characterized by three of these quantum numbers the principal quantum number, the angular momentum quantum number, and the magnetic quantum number. The fourth quantum number (spin quantum number) describes the magnetism of the electron. 

The second rule reflects the importance of the spin quantum number. According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers. The principal, angular momentum, and magnetic quantum numbers specify the energy, shape, and orientation of an orbital. The two values of the spin quantum number reflect the fact that for two electrons to occupy the same orbital, they must have opposite spin states (see Figure 3.2). 

Atomic orbital (AO) (Sections 1.10, 1.11, and 1.15) A volume of space about the nucleus of an atom where there is a high probability of finding an electron. An atomic orbital can be described mathematically by its wave function. Atomic orbitals have characteristic quantum numbers the principal quantum number, n, is related to the energy of the electron in an atomic orbital and can have the values 1, 2, 3,. The azimuthal quantum number I, determines the angular momentum of the electron that results from its motion around the nucleus, and can have the values 0, 1, 2,. .., (n — 1). The magnetic quantum number, m, determines the orientation in space of the angular momentum and can have values from 3-/ to /. The spin quantum number, s, specifies the intrinsic angular... 

From quantum mechanics, you know that there are four quantum numbers ( , the principal /, the orbital m/, the magnetic and m, the spin quantum numbers) that govern the number and types of orbitals that electrons can occupy. Each of these quantum numbers has only certain allowed values for example, n can only be a positive integer (1,2, 3, 4,...) and for each value of n, I can only have values of 0,1,2, up to - 1. These allowed values tell us what orbitals exist. For example, 3d n = 3,1 = 2) exists but 2d n =2,1= 2) does not. An additional rule tells us that for each value of /, there are 2/ + 1 allowed values of OT, and so forth. This rule means that there are always... 

The bound states (where < 0) are characterized by the three quantum numbers n (the principal quantum number), I (the azimuthal quantum number) and mi (the magnetic quantum number). 

Quantum numbers The four quantum numbers—principal, angular momentum, magnetic, and spin—arise from solutions to the wave equation and govern the electron configuration of atoms. 

The angular momentum quantum number is denoted /. It also affects the energy of the electron, but in general not as much as the principal quantum number does. In the absence of an electric or magnetic field around the atom, only these two quantum numbers have any effect on the energy of the electron. The value of / can be 0 or any positive integer up to, but not including, the value of n for that electron. 

From the mathematical restrictions on the solution of the equations comes a set of constraints known as quantum numbers. The first of these is n, the principal quantum number, which is restricted to integer values (1, 2, 3,. ..). The second quantum number is 1, the orbital angular momentum quantum number, and it must also be an integer such that it can be at most (n — 1). The third quantum number is m, the magnetic quantum number, which gives the projection of the 1 vector on the z axis as shown in Figure 2.2. 

The principal interaction experienced is the Zeeman interaction (Hz), which describes the interaction between the magnetic moment of the nucleus and the externally applied magnetic field, B0 (tesla). The nuclear magnetic moment, p (ampere meter2) is proportional to the nuclear spin quantum number (/) and the magnetogyric ratio (y, radian telsa-1 second-1) ... 

Figure 10.5 Energy levels of atomic orbitals, n is the principal quantum number, and the 5, p, d notation indicates the azimuthal quantum number (/). For / = 1 and above the orbital is split into multiple suborbitals (indicated by the number of lines), corresponding to the values of the magnetic quantum number m Each of these lines can hold two electrons (corresponding to spin up and spin down ), giving rise to the rules for filling up the orbitals.

Three quantum numbers had been proposed, based on spectral lines and inferences about electron energy levels a principal quantum number to specify energy level of the atom an azimuthal quantum number to specify the angular momentum of electrons moving elliptically and an inner or magnetic quantum number to express the orientation of the plane of the electron s orbit in a magnetic field. 20... 

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... 

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. 

Almost all the parameters yielded by the various types of radiofrequency spectroscopy arise from the interaction of nuclear magnetic or electrostatic moments with the magnetic or electrostatic fields produced by the surrounding electrons. A consideration of the way these interactions arise shows that they fall into two groups one of the groups contains terms proportional to the electron density at the nucleus, N, itself, Vn(0), and consequently reflects only the s-character of the wave-function centered on N, v>n while the other is proportional to the value for all or some of the electrons surroimding the nucleus N (Table 1). This latter term vanishes for s-type orbitals and for p, d, f orbitals of the same principal quantum number has values in the order p > > d > > f. In practice this means that in a first approximation, only p-electrons contribute to and that the direct effect of the d-orbitals is only... 

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