How does the size of an atom affect its electric field energy?

[jmb741]

cant solve this problem please help.

1a) The hydrogen atom has a single electron in a fixed orbit around the proton with a radius of (5.29 E-11 m). Find the total electric field energy U(E) for the electron and proton assumming that each one has a radius of (1.00E-15 m).

1b) Included the additional contribution to the electrical potential energy U'(E) if we consider the charge within the proton as a uniform charge distribution.

 

[OlderDan]

Electric field energy density is

$$u=e_0E^2/2$$

The numbers give you the separation of the charges, and I assume the radii are to be used to treat the charge as distributed over the surface in part a) and then uniformly distributed for the proton in part b)

You might get something helpful reading a couple of pages here.

http://www.phys.ufl.edu/~rfield/classes/spring01/images/chp31_3.pdf
http://www.phys.ufl.edu/~rfield/classes/spring01/images/chp31_4.pdf
http://www.physics.gla.ac.uk/~dland/ELMAG305/Elmag305txt3.pdf

 

[thepatientmental]

The size of an atom does not directly affect its electric field energy. The electric field energy of an atom is determined by the distribution of charge within the atom and the distance between the charges. However, the size of an atom can indirectly affect its electric field energy by influencing the distribution of charge within the atom.

In the case of the hydrogen atom described in the problem, the size of the atom is given by the radius of the electron's orbit and the radius of the proton. These values are used to calculate the total electric field energy (U(E)) of the atom, which is the sum of the electric potential energies of the electron and the proton.

However, if we consider the charge within the proton as a uniform distribution, this will add an additional contribution to the electric field energy (U'(E)). This is because the uniform distribution of charge will create a more complex electric field, resulting in a higher electric field energy.

To solve the problem, the given values of the radius of the electron's orbit and the proton can be used to calculate the electric field energy (U(E)) using the formula U(E) = kq1q2/r, where k is the Coulomb's constant, q1 and q2 are the charges of the electron and proton respectively, and r is the distance between them.

For part 1b, the additional contribution to the electric field energy (U'(E)) can be calculated by considering the uniform charge distribution within the proton. This can be done using the formula U'(E) = (3/5)kq1q2/r, where the factor (3/5) takes into account the distribution of charge within the proton.

In conclusion, the size of an atom does not directly affect its electric field energy, but it can indirectly influence it by affecting the distribution of charge within the atom.