What is the nuclear spin of this atom?

[unscientific]

Homework Statement

A singly ionized atom exhibits hyperfine structure in a ##^3P_1 \rightarrow ^3S_1## transition. Assuming ##I## is greater than ##J## and given that the ##^3S_1## levels are split by ##66~GHz## and ##54~GHz##, find the nuclear spin ##I##.

Homework Equations

[tex]E_{HFS} = \frac{A}{2} \left[ F(F+1) - I(I+1) - J(J+1) \right] [/tex]

The Attempt at a Solution

Since ##J=1##, the ##^3S_1## level is split by the higher level ##F=I+1## and lower level ##F = I##.

[tex] \frac{(I+1)(I+2) - I(I+1) - J(J+1)}{I(I+1) - I(I+1) - J(J+1)} = \frac{66}{54}[/tex]
[tex] \frac{2I}{2} = 1.22[/tex]

I get ##I = 1.22##, which is strange as shouldn't nuclear spin be either in multiples of ##\frac{1}{2}##?

 

[unscientific]

Solved.