Which neutral atom is isoelectronic with each of the following ions? \(\mathrm{Ga} ^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \mathrm{I}^{-}, \mathrm{Pb}^{2+}.\)

Recall the atomic number of the given elements. The atomic number is equal to the number of protons in the nucleus of an atom and determines the number of electrons a neutral atom possesses. Thus, the number of electrons in each ion can be calculated by subtracting or adding the corresponding charge to the atomic number.

Subtract or add the charge value to the given atomic number to determine the number of electrons in each of the ions: \(\mathrm{Ga} ^{3+}\): Ga has an atomic number of 31. Since it has a charge of +3, it has lost 3 electrons. Therefore, Ga3+ has 31 - 3 = 28 electrons. \(\mathrm{Zr}^{4+}\): Zr has an atomic number of 40. Since it has a charge of +4, it has lost 4 electrons. Therefore, Zr4+ has 40 - 4 = 36 electrons. \(\mathrm{Mn}^{7+}\): Mn has an atomic number of 25. Since it has a charge of +7, it has lost 7 electrons. Therefore, Mn7+ has 25 - 7 = 18 electrons. \(\mathrm{I}^{-}\): I has an atomic number of 53. Since it has a charge of -1, it has gained 1 electron. Therefore, I- has 53 + 1 = 54 electrons. \(\mathrm{Pb}^{2+}\): Pb has an atomic number of 82. Since it has a charge of +2, it has lost 2 electrons. Therefore, Pb2+ has 82 - 2 = 80 electrons.

Now, identify neutral atoms that have the same number of electrons as the given ions: \(\mathrm{Ga} ^{3+}\): A neutral atom with 28 electrons has an atomic number of 28. The element with atomic number 28 is Nickel (Ni). \(\mathrm{Zr}^{4+}\): A neutral atom with 36 electrons has an atomic number of 36. The element with atomic number 36 is Krypton (Kr). \(\mathrm{Mn}^{7+}\): A neutral atom with 18 electrons has an atomic number of 18. The element with atomic number 18 is Argon (Ar). \(\mathrm{I}^{-}\): A neutral atom with 54 electrons has an atomic number of 54. The element with atomic number 54 is Xenon (Xe). \(\mathrm{Pb}^{2+}\): A neutral atom with 80 electrons has an atomic number of 80. The element with atomic number 80 is Mercury (Hg).

The neutral atoms isoelectronic with the given ions are: - \(\mathrm{Ga} ^{3+}\) is isoelectronic with Nickel (Ni). - \(\mathrm{Zr}^{4+}\) is isoelectronic with Krypton (Kr). - \(\mathrm{Mn}^{7+}\) is isoelectronic with Argon (Ar). - \(\mathrm{I}^{-}\) is isoelectronic with Xenon (Xe). - \(\mathrm{Pb}^{2+}\) is isoelectronic with Mercury (Hg).