The isotopic shift (also called isotope shift) is the shift in various forms of spectroscopy that occurs when one nuclear isotope is replaced by another.
NMR spectroscopy
In NMR spectroscopy, isotopic effects on chemical shifts are typically small, far less than 1 ppm, the typical unit for measuring shifts. The 1H NMR signals for 1H2 and 1H2H ("HD") are readily distinguished in terms of their chemical shifts. The asymmetry of the signal for the "protio" impurity in CD2Cl2 arises from the differing chemical shifts of CDHCl2 and CH2Cl2.
Vibrational spectra Isotopic shifts are best known and most widely used in vibration spectroscopy, where the shifts are large, being proportional to the ratio of the square root of the isotopic masses. In the case of hydrogen, the "H-D shift" is (1/2)1/2 ≈ 1/1.41. Thus, the (totally symmetric) C−H and C−D vibrations for CH4 and CD4 occur at 2917 cm−1 and 2109 cm−1 respectively. This shift reflects the differing reduced mass for the affected bonds.
Atomic spectra Isotope shifts in atomic spectra are minute differences between the electronic energy levels of isotopes of the same element. They are the focus of a multitude of theoretical and experimental efforts due to their importance for atomic and nuclear physics. If atomic spectra also have hyperfine structure, the shift refers to the center of gravity of the spectra. From a nuclear physics perspective, isotope shifts combine different precise atomic physics probes for studying nuclear structure, and their main use is nuclear-model-independent determination of charge-radii differences. Two effects contribute to this shift:
Mass effects The mass difference (mass shift), which dominates the isotope shift of light elements. It is traditionally divided into a normal mass shift (NMS) resulting from the change in the reduced electronic mass, and a specific mass shift (SMS), which is present in multi-electron atoms and ions. The NMS is a purely kinematical effect, studied theoretically by Hughes and Eckart. It can be formulated as follows: In a theoretical model of an atom, which has an infinitely massive nucleus, the energy (in wavenumbers) of a transition can be calculated from Rydberg formula:
ν ~ ∞ = R ∞ ( 1 n 2 − 1 n ′ 2 ) , {\displaystyle {\tilde {\nu }}_{\infty }=R_{\infty }\left({\frac {1}{n^{2}}}-{\frac {1}{n'^{2}}}\right),}
where n {\displaystyle n} and n ′ {\displaystyle n'} are principal quantum numbers, and R ∞ {\displaystyle R_{\infty }} is Rydberg constant. However, for a nucleus with finite mass M {\displaystyle M} , reduced mass is used in the expression of the Rydberg constant instead of the electron mass:
ν ~ = ν ~ ∞ M m e + M . {\displaystyle {\tilde {\nu }}={\tilde {\nu }}_{\infty }{\frac {M}{m_{e}+M}}.}
For two isotopes with atomic masses approximately A ′ m u {\displaystyle A'm_{u}} and A ″ m u {\displaystyle A''m_{u}} , where m u {\displaystyle m_{u}} is the unified atomic mass unit, the difference in the energies of the same transition is
… excerpt ends here. Continue reading the full article.
