Final answer:
The energy required to separate an electron from a proton that is 250.0 pm away is -7.22 × 10^-18 J.
Step-by-step explanation:
The energy required to completely separate an electron from a proton can be calculated using the electrostatic potential energy equation.
The formula for electrostatic potential energy is:
PE = \dfrac{kQ_1Q_2}{r}
Where PE is the electrostatic potential energy, k is the electrostatic constant (8.99 × 10^9 Nm^2/C^2), Q_1 and Q_2 are the charges of the particles, and r is the distance between the particles.
In this case, we have an electron and a proton. The charge of an electron is -1.6 × 10^-19 C, and the charge of a proton is +1.6 × 10^-19 C (they have opposite charges).
The distance between the electron and proton is 250.0 pm, which is equal to 250.0 × 10^-12 m.
Substituting the values into the electrostatic potential energy equation:
PE = \dfrac{(8.99 × 10^9 Nm^2/C^2) × (-1.6 × 10^-19 C) × (1.6 × 10^-19 C)}{250.0 × 10^-12 m}
Simplifying the calculation answers:
PE = -7.22 × 10^-18 J
Therefore, the energy required to completely separate an electron from a proton that is 250.0 pm away is -7.22 × 10^-18 J.