Question

To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of 0.529 × 10−10 m, the average distance between proton and electron in a hydrogen atom. How much work is done?

Answer 1

Given Information:

distance between electron and proton = d = 0.529x10⁻¹⁰ m

charge on electron = q₁ = -1.60x10⁻¹⁹ C

charge on proton = q₂ = 1.60x10⁻¹⁹ C

Required Information:

Work done = W = ?

Answer:

Work done = 4.35x10⁻¹⁸ Joules

Explanation:

We know that work done is given by

Work done = kq₁q₂/r

Where q₁ is the charge on electron, q₂ is the charge on proton and k is the coulomb constant and its value is 9x10⁹ Nm²/C²

Work done = (9x10⁹*-1.60x10⁻¹⁹*1.60x10⁻¹⁹)/0.529x10⁻¹⁰

Work done = 4.35x10⁻¹⁸ Joules

Therefore, 4.35x10⁻¹⁸ Joules of work is required to bring electron from a distance of 0.529x10⁻¹⁰ m towards the proton to form a hydrogen atom.

Answer 2

Answer:

-4.37 * 10^(-18) J

Explanation:

Parameters given:

Charge of a proton, Qp = 1.6022 * 10^(-19) C

Charge of an electron, Qe = -1.6022 * 10^(-19) C

Distance between proton and electron, d = 0.529 × 10^(−10) m

The amount of work done is given as:

W = F * d

Where F = electrostatic force

d = distance between them

Electrostatic force is given as:

F = (k * Qp * Qe) / d²

F = (9 * 10^9 * 1.6022 * 10^(-19) * -1.6022 * 10^(-19)) / (0.529 × 10^(−10))²

F = -8.26 * 10^(-8) N

Work done will be:

W = -8.26 * 10^(-8) * 0.529 × 10^(−10)

W = -4.37 * 10^(-18) J