The ground state term for a free ion with 3d7 configuration is 4F9/2.

Explanation:
- The configuration of the ion is 3d7. This means that there are seven electrons in the d subshell of the third energy level.
- To determine the ground state term, we need to consider the total angular momentum of the electrons in the d subshell.
- The total angular momentum is given by the vector sum of the individual angular momenta of each electron.
- For the d subshell, the possible values of the individual angular momenta are -2, -1, 0, 1, and 2.
- The total angular momentum can have values ranging from the absolute value of the difference between the sum of the individual angular momenta and the maximum value of the individual angular momenta, to the sum of the individual angular momenta and the maximum value of the individual angular momenta.
- In this case, the sum of the individual angular momenta is -7 + (-6) + (-5) + (-4) + (-3) + (-2) + (-1) = -28.
- The maximum value of the individual angular momenta is 2.
- Therefore, the possible values of the total angular momentum are from the absolute value of the difference between -28 and 2, which is 26, to the sum of -28 and 2, which is -26.
- The ground state term corresponds to the lowest possible value of the total angular momentum.
- In this case, the ground state term is 4F9/2 because it corresponds to a total angular momentum of -9/2.
- The term symbol consists of a number indicating the total angular momentum (4 in this case), followed by a letter indicating the orbital angular momentum (F in this case), and a subscript indicating the value of the total angular momentum (9/2 in this case).