Electric Field Inside a Hydrogen Atom

In summary, a hydrogen atom is made up of a proton and an electron with opposite charges. The electron's charge is "smeared out" into a spherical distribution around the proton, with a charge density of -Q/(pi*a_0^3)*e^(-2r/a_0). The total amount of charge enclosed within a sphere with radius r centered on the proton can be found by integrating the charge density from 0 to r, resulting in +Q*(1+2r/a_0+2*(r/a_0)^2)*e^(-2r/a_0) if r is less than the electron's distance, and 0 if r is greater than the electron's distance."
  • #1
viperassasin
11
0

Homework Statement


A hydrogen atom is made up of a proton of charge + Q=1.60 \times 10^{ - 19}\; {\rm C} and an electron of charge - Q= - 1.60 \times 10^{ - 19}\; {\rm C}. The proton may be regarded as a point charge at r=0, the center of the atom. The motion of the electron causes its charge to be "smeared out" into a spherical distribution around the proton, so that the electron is equivalent to a charge per unit volume of \rho (r)= - {\frac{Q}{ \pi a_{0} ^{3}}} e^{ - 2r/a_{0}} where a_0=5.29 \times 10^{ - 11} {\rm m} is called the Bohr radius

Find the total amount of the hydrogen atom's charge that is enclosed within a sphere with radius r centered on the proton.


Homework Equations





The Attempt at a Solution



do I just try and divide out the volume.
 
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  • #2
Well one can presumably just integrate charge density from 0 to r to get charge enclosed.
 
  • #3
Here's my guess:
between the proton and the electron, the electron's charge cancels out, since there is no charge inside a uniformly charged sphere. So if r is less than the electron's distance than charge = +Q. If r is greater than the electron's distance, outside a uniformly charged sphere, the sphere can be treated as a point mass at the center of the sphere. So outside the electron's position charge = +Q-Q = 0.
 
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1. What is an electric field?

An electric field is a region in which a charged particle experiences a force due to the presence of other charged particles.

2. How is the electric field inside a hydrogen atom described?

The electric field inside a hydrogen atom is described by the Coulomb potential, which is a function of the distance between the electron and the proton.

3. What is the direction of the electric field inside a hydrogen atom?

The electric field inside a hydrogen atom points towards the positively charged proton.

4. How does the electric field inside a hydrogen atom change as the distance from the nucleus increases?

The electric field inside a hydrogen atom decreases as the distance from the nucleus increases, following the inverse square law.

5. Does the electric field inside a hydrogen atom have a specific value?

Yes, the electric field inside a hydrogen atom can be calculated using the Coulomb potential and the charge of the electron and proton. However, the value of the electric field depends on the distance from the nucleus.

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