Final answer:
To determine the electron's acceleration when separated by a distance from a proton, we apply Coulomb's Law to find the electric force and then use Newton's second law to find the acceleration, considering the known values of electron charge and mass.
Step-by-step explanation:
The question asks us to find the magnitude of the electron's acceleration when an electron and a proton are separated by a distance of 5.3 x 10⁻¹¹ m. To calculate this, we need to use Coulomb's Law to find the electric force and then Newton's second law to find the acceleration.
First, we calculate the electric force (F) between the electron and proton using Coulomb's Law:
F = k * |q1 * q2| / d²
where k is Coulomb's constant (8.988 x 10⁹ N m²/C²), q1 and q2 are the charges of the proton and electron (1.602 x 10⁻ C), and d is the separation distance.
After calculating the force, we find the acceleration (a) of the electron using Newton's second law:
a = F / m
where m is the mass of the electron (9.11 x 10⁻1 kg).
Completing these calculations gives us the electron's acceleration.