Final answer:
The total energy of an electron in a hydrogen atom with a given orbit radius can be determined using the formula E = -13.6 eV / n². By calculating the principal quantum number n from the given radius, we can find the total energy of the electron. In this case, the total energy is -3.4 eV.
Step-by-step explanation:
The total energy of an electron in the hydrogen atom can be determined using the formula:
E = -13.6 eV / n²
where E is the energy, n is the principal quantum number, and eV represents electron volts.
Given that the radius of the electron's orbit is 8.784 × 10⁽⁻¹⁰⁾ m, we can find the value of n using the formula for the radius of the nth orbit:
r = 0.529 × n² / Z Å
where r is the radius, n is the principal quantum number, and Z is the atomic number. Assuming the atomic number for hydrogen is 1, solving for n gives us:
n = √(r * Z / 0.529)
Substituting the given values, we find that n = 2.
Finally, plugging in n into the energy formula, we find:
E = -13.6 eV / (2²) = -3.4 eV