Isomeric Shift (Mössbauer Spectroscopy)

 

Definition:

The isomeric shift (also called the chemical shift) in Mössbauer spectroscopy refers to the shift in the energy of gamma rays absorbed or emitted by a nucleus due to the interaction between the nuclear charge distribution and the surrounding electron density. This shift provides insights into the chemical and electronic environment of the nucleus.

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Origin of Isomeric Shift:

1. Interaction:

   • The isomeric shift is caused by the electrostatic interaction between the nuclear charge distribution and the s-electron density at the nucleus.
   • It arises because the nuclear charge radius changes slightly between the ground and excited states.

2. Dependence on Electron Density:

   • The s-electron density at the nucleus is sensitive to chemical bonding, oxidation state, and coordination environment of the atom.

3. Energy Shift:

   • The shift is proportional to the difference in electron density between the source and absorber nuclei.

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Key Parameters:

1. Chemical Information:

   • The isomeric shift provides information on:
     • Oxidation states.
     • Covalency of bonds.
     • Electronic configuration.

2. Unit:

   • Measured in mm/s, typically through Doppler shifts in the experimental setup.

3. Significance:

   • A higher electron density at the nucleus results in a positive isomeric shift.
   • A lower electron density results in a negative isomeric shift.

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Equation:

The isomeric shift ($\delta$) is given by:

$$\delta = \frac{\Delta E}{E} \propto (\rho_{\text{source}} - \rho_{\text{absorber}})$$

where:

• $\rho_{\text{source}}$ = s-electron density at the source nucleus.
• $\rho_{\text{absorber}}$ = s-electron density at the absorber nucleus.

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Applications:

• Identifying oxidation states of elements (e.g., Fe$^{2+}$ vs. Fe$^{3+}$).
• Studying the electronic environment in coordination compounds.
• Probing chemical bonding and covalency.

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Example: Isomeric Shift of $^{57}\text{Fe}$

• Iron Oxides:

  • In Mössbauer spectroscopy, Fe$^{2+}$ has a higher electron density at the nucleus compared to Fe$^{3+}$, leading to a more positive isomeric shift.
  • Typical values:
    • Fe$^{2+}$ in ferrous oxide (FeO): ~1.1 mm/s.
    • Fe$^{3+}$ in ferric oxide (Fe$_2$O$_3$): ~0.3 mm/s.

• High-spin vs. Low-spin States:

  • High-spin Fe$^{2+}$ (more unpaired electrons) generally shows a higher isomeric shift compared to low-spin Fe$^{2+}$ due to increased shielding effects and higher electron density.

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Sample Problem:

Q: Explain how isomeric shifts help distinguish between Fe$^{2+}$ and Fe$^{3+}$ in Mössbauer spectroscopy.

A: Fe$^{2+}$ has a greater electron density at the nucleus compared to Fe$^{3+}$, as it has more electrons in the 3d and 4s orbitals. This increased electron density leads to a higher isomeric shift value for Fe$^{2+}$. In contrast, Fe$^{3+}$, with fewer electrons, shows a smaller isomeric shift. By comparing the isomeric shift values, we can distinguish between the two oxidation states.