The number of allowed EPR lines expected for a metal ion with 3 unpaired electrons and a nuclear spin (I) of 7/2 is

Concept:

The EPR spectrum consists of multiple lines corresponding to different energy transitions of the unpaired electrons. These lines can be characterized by their positions (resonance frequencies), intensities, and shapes. Each line provides insight into the electronic structure and interactions within the paramagnetic species.

Explanation:

Number of lines for EPR can be determined by the equation 

No. Of Lines = unpaired electrons (2nI+1)

where, I = nuclear spin

            n = no. of metals 

Given: 

unpaired electrons = 3

n = 1 (only metal ion is present)

I = 7/2

Calculation:

No. of Lines = 3 X (2 X 1 X 7/2 +1)

No. of Lines = 24 lines

Conclusion:

Hence, the number of lines observed in EPR are 24 lines.