Question

The Bohr radius a0 is the most probable distance between the proton and the electron in the Hydrogen atom, when the Hydrogen atom is in the ground state. The value of the Bohr Radius is: 1 a0 = 0.529 angstrom. One angstrom is 10-10 m. What is the magnitude of the electric force between a proton and an electron when they are at a distance of 2.63 Bohr radius away from each other?

Answer 1

The electric force is
`F = 11.9 *10^(-9) \ N`

Step-by-step explanation:

From the question we are told that

The Bohr radius at ground state is
`a_o = 0.529 A = 0.529 ^10^(-10) \ m`

The values of the distance between the proton and an electron
`z = 2.63a_o`

The electric force is mathematically represented as

`F = (k * n * p )/(r^2)`

Where n and p are charges on a single electron and on a single proton which is mathematically represented as

`n = p = 1.60 * 10^(-19) \ C`

and k is the coulomb's constant with a value

`k =9*10^(9) \ kg\cdot m^3\cdot s^(-4)\cdot A^2.`

substituting values

`F = (9*10^(9) * [(1.60*10^(-19) ]^2))/((2.63 * 0.529 * 10^(-10))^2)`

`F = 11.9 *10^(-9) \ N`