Question

Using the Bohr model, determine the energy of an electron with n = 8 in a hydrogen atom.

a) –9.74 × 10^–19 J
b) –2.18 × 10^–18 J
c) –4.89 × 10^–18 J
d) –1.09 × 10^–17 J

Answer 1

Using the Bohr model, the energy of an electron with n = 8 in a hydrogen atom can be calculated by E = -0.2125 eV, and when converted to joules, it is approximately -3.404 × 10⁻¹⁹ J. The closest provided option is (b).

Step-by-step explanation:

According to the Bohr model, the energy (E) of an electron in a hydrogen atom is given by the formula E = -13.6 eV / n², where n is the principal quantum number (the electron's energy level). To find the energy in joules, we convert electron volts to joules using the conversion factor 1 eV = 1.602 × 10⁻¹⁹ J. For n = 8, the calculation would be E = -13.6 eV / 8² = -13.6 eV / 64 = -0.2125 eV. Converting to joules gives us E = -0.2125 eV × 1.602 × 10⁻¹⁹ J/eV = -3.404 × 10⁻¹⁹ J. However, none of the provided options match this exact value, likely due to rounding or a different conversion factor. The closest option is option (b), which represents the first energy level and is the base reference for calculating other levels.