Question

1) What is the electrostatic potential energy (in joules) between an electron and a proton that are separated by 56 pm?

2) What is the change in potential energy if the distance separating the electron and proton is increased to 1.0 nm?

Answer 1

Answer:

Step 1:

(1) The formula for electrostatic potential is:

U = (1/4πε0) × (qp ×qe/r)

Where, ε₀= permittivity of free space = 8.854187817620 × 10⁻¹²  m^-3 kg^-1 s⁴ A²

qp= proton charge = 1.60217662 × 10^-19 coulombs

qe = electron charge = -1.60217662 × 10^-19 coulombs

r = separation distance = 56 pm = 56 × 10⁻¹² m

So calculating for potential energy U:

U = (1/(4π×8.854187817620 ×10^-12 m^-3 kg^-1 s⁴ A² )) (1.60217662 × 10-19 coulombs ×-1.60217662 × 10-19 coulombs / 56 × 10−12 m)

U = -4.1× 10^-18 Joules

Step 2:

(2)

Given , r = separation distance = 1 nm = 1 × 10^-9 m

so the potential energy (U) will be

U = (1/(4π ×8.854187817620 ×10^ -12 m^-3 kg^-1 s⁴ A²)) (1.60217662 × 10-19 coulombs × -1.60217662 × 10-19 coulombs / 1× 10−9 m )

U = -2.3× 10^-19 Joules