Wikipedia / Isotopic shift
Wikipedia / Isotopic shift
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 1ppm, the typical unit for measuring shifts. The NMR signals for and ("HD") are readily distinguished in terms of their chemical shifts. The asymmetry of the signal for the "protio" impurity in arises from the differing chemical shifts of and .
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 and occur at 2917cm−1 and 2109cm−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 is Rydberg constant.
, reduced mass is used in the expression of the Rydberg constant instead of the electron mass
For two isotopes with atomic masses is the unified atomic mass unit The above equations imply that such mass shift is greatest for hydrogen and deuterium.
The effect of the specific mass shift was first observed in the spectrum of neon isotopes by Nagaoka and Mishima.
Consider the kinetic energy operator in Schrödinger equation
, which gives the normal mass shift formulated above.
which requires the knowledge of an accurate many-electron wave function as the mass of the nucleus increases, same as the normal mass shift.
Volume effects
The volume difference (field shift) dominates the isotope shift of heavy elements. This difference induces a change in the electric charge distribution of the nucleus. The phenomenon was described theoretically by Pauli and Peierls. Adopting a simplified picture, the change in an energy level resulting from the volume difference is proportional to the change in total electron probability density at the origin times the mean-square charge radius difference.
For a simple nuclear model, where A is the atomic mass number is a constant.
Similarly, calculating the electrostatic potential of an ideal charge density
Such a perturbation of the atomic system neglects all other potential effect, like relativistic corrections. Using the perturbation theory (quantum mechanics), only the s
The explicit form for hydrogenic
This equation confirms that the volume effect is more significant for hydrogenic atoms with larger Z, which explains why volume effects dominates the isotope shift of heavy elements.