Final answer:
The distance of the electron from the nucleus in a hydrogen atom can be calculated using the Bohr model. By substituting the energy of the electron in the formula and solving for the principal quantum number, we can then calculate the distance of the electron from the nucleus using the formula for the radius of the orbit.
Step-by-step explanation:
The distance of an electron from the nucleus in a hydrogen atom can be calculated using the Bohr model. According to the Bohr model, the electron orbits the nucleus in circular paths called orbits. The radius of these orbits can be calculated using the formula r = n^2 * (0.529 Å), where n is the principal quantum number.
In this case, the energy of the electron is given as -8.72 × 10^–20 J. The energy of an electron in a specific orbit is given by the equation E = -13.6 eV / n^2, where E is the energy in electron volts and n is the principal quantum number. By rearranging this equation, we can solve for n^2:
n^2 = (-13.6 eV / E)
Substituting the given energy value and solving for n^2:
n^2 = -13.6 eV / (-8.72 × 10^–20 J)
n^2 = 1.56 x 10^21
Taking the square root of both sides to solve for n:
n ≈ 3.95 x 10^10
Now we can substitute the value of n in the formula for the radius:
r = (3.95 x 10^10)^2 * (0.529 Å)
r ≈ 8.16 Å
Therefore, the electron is approximately 8.16 Å away from the nucleus in a hydrogen atom with an energy of -8.72 × 10^–20 J.