Predicting Nuclear Spin (I)
How do you predict the value of nuclear spin (I) based on the number of protons and neutrons?
|
|
|
Across the entire periodic table, nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found. Protons and neutrons each have net spins of ½, but this derives from the elementary quarks and gluons of which they are composed. As a result of this complexity, no simple formula exists to predict I based on the number of protons and neutrons within an atom. Nevertheless, there are some general rules that apply to special cases:
|
Internal structure of the proton: 2 "up" quarks and one "down" quark held together by the strong nuclear force mediated by gluons
|
1) Even/Even. Nuclei containing even numbers of both protons and neutrons have I = 0 and therefore cannot undergo NMR. Examples include 4He,12C,16O and 32S.
2) Odd/Odd. Nuclei with odd numbers of both protons and neutrons have spin quantum numbers that are positive integers. Examples include14N (I=1),2H (deuterium, I=1), and10B (I=3).
3) All others. The remaining nuclei (odd/even and even/odd) all have spins that are half integral. Examples include 1H (I=½), 17O (I=5/2), 19F (I=½), 23Na (I=3/2), and 31P (I=½).
Every element in the periodic table has at least one isotope that can experience NMR when placed in a magnetic field. For odd-numbered elements this is the isotope with highest natural abundance. For even-numbered elements, the principal isotope will nearly always have I=0, but there will be one or more less abundant isotopes that are NMR-active.
For example, the most common naturally occurring isotope of carbon (¹²C) contains 6 protons and 6 neutrons. According to Rule #1 above, ¹²C has I = 0 and cannot undergo NMR. However, carbon's ¹³C isotope (natural abundance 1.07%) contains one extra neutron, resulting in a net spin (I =½) and permitting its use in NMR.
The illustration below shows the distribution of nuclear spin (I) values for principal NMR active isotopes across the periodic table. Some additional "fun facts" about spin are included in the Advanced Discussion section for those interested chemists among you!
For example, the most common naturally occurring isotope of carbon (¹²C) contains 6 protons and 6 neutrons. According to Rule #1 above, ¹²C has I = 0 and cannot undergo NMR. However, carbon's ¹³C isotope (natural abundance 1.07%) contains one extra neutron, resulting in a net spin (I =½) and permitting its use in NMR.
The illustration below shows the distribution of nuclear spin (I) values for principal NMR active isotopes across the periodic table. Some additional "fun facts" about spin are included in the Advanced Discussion section for those interested chemists among you!
References
Grushow A. NMR Periodic Table (website). Rider University, 2003. (An interesting set of periodic tables that allow you to explore elements sorted by NMR frequency, spin, receptivity, and natural abundance).
Moskowitz C. Proton spin mystery gains a new clue. Scientific American online, Jul 21, 2014. (the important role of gluons in contributing to proton spin)
Parella T. eNMR: NMR Periodic Table (website), 2003. (A fairly complete table with hyperlinks giving NMR properties of approximately 80 elements and their isotopes).
Wood C, Sherman M. Inside the proton, the ‘most complicated thing you could possibly imagine.' Quanta Magazine, October, 2022. [LINK FOR MULTIMEDIA VERSION]
Winter M. WebElements Periodic Table (website), 2013. (A more complete table of all the elements with all their physical properties, including many of the newer, collider-generated ones with atomic numbers > 105. Although NMR data for these elements is lacking, they have non-zero spins and in theory should undergo NMR).
Grushow A. NMR Periodic Table (website). Rider University, 2003. (An interesting set of periodic tables that allow you to explore elements sorted by NMR frequency, spin, receptivity, and natural abundance).
Moskowitz C. Proton spin mystery gains a new clue. Scientific American online, Jul 21, 2014. (the important role of gluons in contributing to proton spin)
Parella T. eNMR: NMR Periodic Table (website), 2003. (A fairly complete table with hyperlinks giving NMR properties of approximately 80 elements and their isotopes).
Wood C, Sherman M. Inside the proton, the ‘most complicated thing you could possibly imagine.' Quanta Magazine, October, 2022. [LINK FOR MULTIMEDIA VERSION]
Winter M. WebElements Periodic Table (website), 2013. (A more complete table of all the elements with all their physical properties, including many of the newer, collider-generated ones with atomic numbers > 105. Although NMR data for these elements is lacking, they have non-zero spins and in theory should undergo NMR).