4n + 3 series

Both a 4n and a 4n + 3 series of heavy radioactive elements occur naturally. The 4n series is sometimes called the thorium series, since its long-lived parent is Th232 (half-life, 14,000,000,000 years), whereas the 4n + 3 series is the actinium series. The long-lived parent of the latter is U235 (half-life 707,000,000 years), but unlike the 4n + 2 series, one of its members is actinium (Ac227). Final members of both of these series are lead isotopes, Pb208 and Pb207. 

There are four such series of naturally occurring isotopes. The series in which aU mass numbers are evenly divisible by 4 is called the 4n series. The series with mass numbers 1 more than the corresponding 4n series members is called the 4n + 1 series. Similarly, there are a 4n -f 2 series and a 4n -f 3 series. Since the mass numbers change by 4 or 0, no member of any series can produce a product in a different series. 

The 4n series - the thorium series The 4n + 1 series — the neptunium series The 4n + 2 series = the uranium-radium series The 4n + 3 series - the uranium-actinium series... 

Each of the uranium isotopes is a member of one of the four possible radioactive decay series involving successive alpha and beta decay reactions. is the longest-lived member and the parent of the 4n -t- 2 series, which includes as a member. is the longest-lived member and the natural parent of the 4n + 3 series, decays by alpha emission to Th, the longest-lived member and natural parent of the 4n series, to be described in Chaps. 6 and 8. decays by alpha emission to Th, also a member of the 4n series. Problems arising from the radioactivity of and its daughters are discussed in Chap. 8. U decays by beta emission to Np, the longest-lived member of the 4n -I- 1 series, the only one not of natural occurrence. is an intermediate member of this series. 

From a more detailed analysis of MO and state correlation diagrams. Woodward and Hoffmann presented a set of selection rules for cycloaddition reactions, which are summarized in Table 11.1. ° Here p and q are the number of electrons in the two n systems imdergoing the cycloaddition reaction. When the sum of p and g is a member of the 4n series, then the reaction is thermally allowed to be suprafacial with respect to one of the n components and antarafacial with respect to the other one. When the sum of p and qisa member of the 4n -h 2 series, then Ihe reaction is thermally allowed when it is either suprafacial with respect to both components or antarafacial with respect to both. As usual, the selection rules are reversed for photochemical reactions. 

O Table 13.1 shows the a-decay energies of the 4n series and the energies predicted by the semiempirical equation without shell effects. The equation agrees with the facts near the middle — at °Rn. The predicted half-lives are too short in the Th—U region, and too long for Po (just above the shell). The Hg—Pb isotopes are predicted to have rather short half-lives for Qt decay. To be sure some of them are energetically unstable, but not enough that barrier penetration proceeds at an appreciable rate. 

Growth and decay of Ra after isolation of radium from 4n series at secular equilibrium. The top curve gives the decay of Ra after the first isolation relative to the secular rate. The growth curve shows the time dependence of Ra that comes from Ra (via Ac and Th). The middle decay curve shows Ra that decays (with the clock restarted) after thorium is removed when growth and decay are equal (about 22 days from t = 0). The bottom decay curve shows decay following a third purification (about 10 days after the second]... 

FIGURE 1.5 The natural radioactive decay chain of the 4n series, beginning with thorium-232 and ending with lead-208. 

Just as the uranium series is called the "An + 2" series, the thorium series can be called the "4n" series and the actinium series the "An + 3" series. A "An + 1" series has also been established, with glPu as the parent nuclide. To which series does each of the following belong (a) gtBi (b)... 

For normal commercial-quality mild steels in the annealed or normalised conditions in which they are almost invariably used, various workers have shown that the carbon content of the steel is the major factor determining intergranular cracking susceptibility. Figure 8.13 shows the threshold stresses for a series of commercial mild steels of different carbon contents caused to crack in boiling 4n NH4NO3. The trend of the result suggests... 

Conjugation of the 7t-electrons of the carbon-carbon double bond with the LUMO sulfur 3d-orbitals would be expected to stabilize the Hiickel 4n -I- 2 (n = 0) array of n-electrons in the thiirene dioxide system. No wonder, therefore, that the successful synthesis of the first member in this series (e.g. 19b) has initiated and stimulated several studies , the main objective of which was to determine whether or not thiirene dioxides should be considered to be aromatic (or pseudo-aromatic ) and/or to what extent conjugation effects, which require some sort of n-d bonding in the conjugatively unsaturated sulfones, are operative within these systems. The fact that the sulfur-oxygen bond lengths in thiirene dioxides were found to be similar to those of other 802-containing compounds, does not corroborate a Hiickel-type jr-delocalization... 

The composition, reaction conditions, and yield of copolymer-1 (24-37 series ) are shown in Table 12. The content of 4N,4N-dimethyl-4-ammoniumhept-1,6-diene chloride in the reaction ranges from 0 to 30 molar percent of total monomer content. The concentration of lignin, calcium chloride, and monomer in the... 

The origin of cyclopropenone chemistry goes back to the successful preparation of stable derivatives of the cyclopropenium cation <5 3), the first member of a series of Huckel-aromatic monocyclic carbo-cations possessing a delocalized system of (4n + 2)-7r-electrons. This experimental confirmation of LCAO-MO theory stimulated efforts to prepare other species formally related to cyclopropenium cation by a simple resonance description of electron distribution, namely cyclopropenone 7 and methylene cyclopropene (triafulvene) 8 ... 

The phthalocyanine [1-4] system is structurally derived from the aza-[18]-annulene series, a macrocyclic hetero system comprising 18 conjugated n-electrons. Two well known derivatives of this parent structure, which is commonly referred to as porphine, are the iron(III)complex of hemoglobin and the magnesium complex of chlorophyll. Both satisfy the Htickel and Sondheimer (4n + 2)- electron rule and thus form planar aromatic systems. 

FLF)- (L = H or D) anion in low temperature solutions of (C4H9)4N+ (FL)nF . The authors were able to determine zero-, one-, and two-bond, H/D isotope effects on hydrogen and fluorine NMR chemical shifts for the series n = 1 to n = 3, and to relate the observed spectra to H/D isotope effects on the hydrogen bond geometries. Isotope effects on spin-spin L-F and F-F coupling 13C constants were reported. 

All elements with Z > 83 (Bi) are unstable and belong to chains of radioactive decay, or decay series. Three decay series include all radioactive elements in the Z > 83 part of the chart of nuclides—namely, 4n, 4n + 2, and 4n + 3 (because the decay takes place by a emission with mass decrease of four units, or by jS emission with a negligible mass decrease, all nuclides within a series differ by... 

Limiting ourselves to the observation of isotopic abundances determined by the 4n + 2 and 4n + 3 decay series, we can construct a concordia diagram (Wetherill, 1956) relating (206p /238 j 207pj /235 j ratios developing at... 

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