Final answer:
The lowest possible energy for an electron in the Li²⁺ ion using the Bohr model is calculated to be -1.96 × 10⁻ J, which does not match any of the provided options. There seems to be an error in the options given.
Step-by-step explanation:
To determine the lowest possible energy, in joules, for an electron in the Li²⁺ ion using the Bohr model, we can use the formula that gives the energy levels of the hydrogen-like ions:
E = -{(Z² × 13.6 eV/n²} × 1.602 × 10⁻¹⁹ J/eV
Where:
- Z is the atomic number of the ion.
- n is the principal quantum number of the electron's orbit.
For the Li²⁺ ion, Z = 3 (since lithium has an atomic number of 3) and n = 1 (the lowest possible energy level). Then we plug in the values into the equation:
E = -{(3² × 13.6 eV) / (1²)} × 1.602 × 10⁻¹⁹ J/eV
= -{(9 × 13.6 eV)} × 1.602 × 10⁻¹⁹ J/eV
= -122.4 eV × 1.602 × 10⁻¹⁹ J/eV
= -1.96 × 10⁻ J
The energy is negative because it represents the bound state of an electron; the more negative the energy, the more tightly the electron is bound to the nucleus. Thus, the lowest possible energy for an electron in the Li²⁺ ion using the Bohr model is -1.96 × 10⁻ J.
Hence, the correct answer would be none of the choices given, as there seems to be an error in the options provided. The calculation presented here reflects the proper application of the Bohr model for the Li²⁺ ion.