Final answer:
The electron is in the 7th Bohr orbit of the hydrogen atom.
Step-by-step explanation:
The energy of an electron in a hydrogen atom is given by the formula E = -13.6 eV/n^2, where n is the principal quantum number or the number of the Bohr orbit.
In this case, we can rearrange the formula to solve for n^2. Given that the energy of the electron is -4.45 × 10^-20 J, we can convert it to electron volts (eV) using the conversion factor 1 eV = 1.6 × 10^-19 J.
Substituting the values into the formula, we have: -4.45 × 10^-20 J = -13.6 eV/n^2. Solving for n^2,
we find:
n^2 = (-13.6 eV)/(-4.45 × 10^-20 J).
Converting -4.45 × 10^-20 J to eV, we get -4.45 × 10^-20 J × (1 eV/1.6 × 10^-19 J) = -0.278 eV.
Substituting this value back into the formula, we have:
n^2 = (-13.6 eV)/(-0.278 eV) = 48.92.
Taking the square root of both sides, we find:
n = √(48.92) ≈ 6.99.
Therefore, the electron is in the 7th Bohr orbit.