Electric Field Energy of Hydrogen Atom: Proton & Electron

[bertholf07]

Electric Field Energy?

Cant solve this problem please help?

(Given)The Classical model of the hydrogen atom has a single electon in a fixed orbit around the proton with the bohr radius (5.29E-11 m). It is assumed that the Coulomb force between the proton and the electron holds the hydrogen atom together. However, this is not completely true since both the proton and the electron have a mass so that Newton's Law of universal gravitation provides also an attactive force.

(Question 1)An improvement of this classical mechanical model of the atom involves the energy density of the electric field u(E) in a region of space. Fine the total electric field energy U(E) for the electron and proton assuming that each on has a radius of 1.00E-15?

(Question 2)Include the additional contribution to the electrical potential energy U'(E) if we consider the charge within the proton as a uniform charge distribution.

 

[Doc Al]

Please do not double post!

Once is enough: https://www.physicsforums.com/showthread.php?t=73235

 

[ravenprp]

The electric field energy of a hydrogen atom can be calculated by considering the potential energy between the proton and electron. This potential energy is given by the Coulomb force equation, where the electric field strength is inversely proportional to the distance between the two particles.

(Question 1) To find the total electric field energy, we need to consider the electric field strength at the surface of both the proton and electron. Since the radius of each particle is given as 1.00E-15, we can calculate the electric field strength using the equation E = kq/r^2, where k is the Coulomb constant (8.99E9 Nm^2/C^2), q is the charge of the particle, and r is the radius.

For the proton, the electric field strength would be E = (8.99E9)(1.60E-19)/((1.00E-15)^2) = 1.44E6 N/C.
Similarly, for the electron, the electric field strength would be E = (8.99E9)(-1.60E-19)/((1.00E-15)^2) = -1.44E6 N/C.

Now, we can calculate the total electric field energy using the formula U(E) = qE, where q is the charge of the particle and E is the electric field strength. For the proton, U(E) = (1.60E-19)(1.44E6) = 2.30E-13 J. For the electron, U(E) = (-1.60E-19)(-1.44E6) = 2.30E-13 J.

Therefore, the total electric field energy of the hydrogen atom is 4.60E-13 J.

(Question 2) If we consider the charge within the proton as a uniform distribution, we need to use the equation U'(E) = (3/5)(kq^2)/r, where r is the radius of the charge distribution. In this case, r = 1.00E-15 m.

Substituting the values for k and q, we get U'(E) = (3/5)((8.99E9)(1.60E-19)^2)/(1.00E-15) = 2.87E-28 J.

Therefore, the additional contribution to the electric field energy