In Mossbauer spectrum of a sample containing iron recorded in the presence of a static magnetic field, the number of possible allowed transition(s) is

Concept:

Mössbauer spectroscopy:

This technique is used in solid-state physics and chemistry to study the characteristics of atomic nuclei in a material. It is a type of gamma-ray spectroscopy that offers comprehensive details on the electrical and magnetic environment around particular atomic nuclei.

A sample, radioactive source like iron-57 is often exposed to a source of gamma rays in Mössbauer spectroscopy. The sample's nuclei absorb the gamma rays, which causes the nuclei to get excited to higher energy states. In mineralogy, this method is frequently used to determine the valence state of iron whether it's Fe(0), Fe(II) or (III).

Explanation:

The magnetic dipole selection rule for Mössbauer spectroscopy is,

\(\Delta m_{I}=0,\pm1\)  ,where m_I= magnetic quantum no.

for quadruple splitting, \(I> \frac{1}{2} (G.S./E.S.)\) , where I= nuclear spin

\(57Fe=(I_{G.S}=\frac{1}{2}) \:and(I_{E.S}=\frac{3}{2})\)

\(Fe(spin G.S.)=\frac{1}{2} \), degeneracy for G.S=\((2nI+1)\)

=\((2\times1\times\frac{1}{2})+1=2\)

\(Fe(spin E.S.)=\frac{3}{2} \), degeneracy for E.S=\((2\times1\times\frac{3}{2})+1=4\)

Mössbauer lines in ⁵⁷Fe in the presence of static magnetic field=\(2+4=6\)

Conclusion:

Hence the correct answer is Six.