Quantum numbers first

First Quantum Number, n Principal Energy Levels... 

When tlte first quantum number takes the value one, the second quantum number can only be zero and likewise toe third quantum number. Now according to Pauli s exclusion principle it is forbidden for more than one electron in a. shell, therefore having the same n value, to have the same values for the remaining three quantum numbers. This gives the prediction that a maximum of two electrons occupy the first shell and that these share the same first three quantum numbers but differ in the value of the fourth, adopting one of two values. For the n 2 shell the situation is more complicated, since there are two possible values for the second quantum number, namely one and zero (as shown in Figure 6). When the second quan-... 

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.

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 first quantum number is the principle quantum number (n) that describes the size of the orbital and relative distance from the nucleus. The possible values of n are positive integers (1,2,3,4, and so on). The smaller the value of n, the lower the energy, and the closer the orbital is to the nucleus. We sometimes refer to the principle quantum number as designating the shell the electron is occupying. 

Each wave function is defined by a set of quantum numbers. The first quantum number, the principal quantum number n, generally relates to the distance of the electron from the nucleus, and hence the energy of the electron. It divides the orbitals into groups of similar energies called shells. The principal quantum number also defines the row occupied by the atom in the periodic table. It has integral values, n = 1, 2, 3, 4, etc. The numerical values are used to describe the shell. 

First Quantum Number Second Quantum Number Notation for Subsbells... 

Fig. 13.6. Calculated branching ratios cth+oh/ d+OH following the photodissociation of the 0m) (m = 0,2 and 4) vibrational states of HOD through the first continuum. The first quantum number gives the excitation of the O-D bond (n = 0 in the present case) and the second one, m, indicates excitation of the O-H bond. The open circle is the experimental result of Shafer, Satyapal, and Bersohn (1989) for the photolysis of 00) at 157 nm. The filled circle is the result for initial state 04) and photolysis wavelength A2 = 218.5 nm and the (upward) arrow indicates the lower limit for state 04) and A2 = 239.5 nm. See Figure 11.7 for an illustration of the experimental set-up. The arrow on the energy axis marks the energy of the barrier of the 4-state PES. E = 0 corresponds to three atoms in their ground state. Reproduced from Vander Wal et al. (1991).

The first quantum number is called the principal quantum number and describes the energy level. These quantum numbers are integers beginning with 1. The first energy level is closest to the nucleus, and each successive energy level is farther from the nucleus (Figure 8.8). 

The first number is called the principal quantum number, n, and it can be any whole number integer. The first quantum number, n, represents the principal energy level that the electron in question is in. For example the one electron in H is Is1 and n will equal 1. The valence electron of Li, ls s1, will have n equal to 2. 

The spectrum (10.1.1) defines a doubly infinite sequence of states. They can be organized into series labelled by the first quantum number N. The states within a series are labelled by N. The first 12 series are shown in Fig. 10.1. For energies larger than Ejf, electron number 2 ionizes. Thus, every Rydberg series in Fig. 10.1 possesses an ionization continuum, which is also sketched. 

The rooms in many buildings contain numbers on their doors, so that they can be found easily. So to, numbers are given to electrons, so that we can picture where they are likely to be found. The numbers that are given to electrons are called quantum numbers, and each electron is given four. n The principal, or first, quantum number is used to indicate the energy level that the electron is found in. The value for n will always be a whole number, and the higher the number, the further away from the nucleus the electron described by n tends to be. For example, an electron with a value of 3 for n is in the third energy level, so it is likely to be located further away from the nucleus than an electron with a value of 1 for n. 

First Quantum Number Principal n Energy Level 1-7... 

The first quantum number is the principal quantum number, n. The principal quantum number designates the shell level. The larger the principal quantum number, the greater tire size and energy of the electron orbital. For the representative elements the principal quantum number for electrons in the outer most shell is given by the period in the periodic table. The principal quantum number for tire transition metals lags one shell behind the period, and for the lanthanides and actinides lags two shells behind tire period. 

When the first quantum number, or n, takes the value of 1, the second quantum number can only be 0, and hkewise the third quantum number (table 7.7). According to Pauli s principle, the first shell can therefore contain a maximum number of two electrons that differ just in the value of the fourth quantum number. 

This more sophisticated explanation for the periodic system is provided in terms of the relationship between the four quantum numbers that can be assigned to any electron in a many-electron atom. The first quantum number n can adopt any integral value starting with 1. The second quantum number which is given the label t can have any of the following values related to the values of n,... 

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