An electron and a proton are initially very far apart (effectively an infinite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of 5.40 10-11 m. What is EPEfinal - EPEinitial, which is the change in the electric potential energy?
P.E change = k*e/R
where k is the Coulomb's Law constant, e is the electron charge, and R = 5.4*10^-11 m
To find the change in electric potential energy (EPE), we need to calculate the initial and final EPE values and then subtract them.
The electric potential energy (EPE) of two charges can be calculated using the formula:
EPE = k * (q1 * q2) / r
Where:
- k is the Coulomb's constant (k ≈ 9.0 x 10^9 N m²/C²)
- q1 and q2 are the charges of the particles (electron and proton in this case)
- r is the separation between the charges
Since the electron and proton are initially very far apart (effectively an infinite distance apart), we can consider their initial EPE to be zero.
Now, let's calculate the final EPE when the electron is orbiting the proton at an average distance of 5.40 * 10^-11 m.
Step 1: Calculate the charge of the electron and proton:
- The charge of an electron (q1) is -1.6 x 10^-19 C (negative due to its negative charge).
- The charge of a proton (q2) is +1.6 x 10^-19 C (positive due to its positive charge).
Step 2: Calculate the final EPE:
- r = 5.40 x 10^-11 m (distance between electron and proton)
EPEfinal = k * (q1 * q2) / r
Substituting the values:
EPEfinal = (9.0 x 10^9 N m²/C²) * (-1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5.40 x 10^-11 m)
Step 3: Calculate EPEfinal - EPEinitial:
Since the initial EPE is zero (EPEinitial = 0), we can simplify the equation:
EPEfinal - EPEinitial = EPEfinal - 0
EPEfinal - EPEinitial = EPEfinal
Therefore, the change in electric potential energy (EPEfinal - EPEinitial) is equal to the final electric potential energy (EPEfinal) we calculated.
Now you can calculate EPEfinal using the formula above and provide the final answer.