Question

In: Physics

An electron in a hydrogen atom orbits the proton at a radius of 5.29 x 10-11...

An electron in a hydrogen atom orbits the proton at a radius of 5.29 x 10^-11 m. Considering the proton to be at the origin, and answering to 2 decimal places:

(a) What is the electric field due to the proton at the position of the electron? (answer in terms of r, theta, and phi).

(b) What is the resultant force on the electron? (answer in terms of r, theta, and phi).

(c) What is the magnitude of the resulting acceleration?

(d) If the electron in the hydrogen atom is in a bound state, and is therefore undergoing circular motion where the Coulomb force holding it in the atom is equal to the central force of circular motion, what is the electron velocity as it orbits the atom?

Expert Solution

We consider the proton to be a point mass and it is situated at the origin.

Now the radius of the electron orbital is

Now the charge of the proton and the charge of a electron is

a) So the electric field due to proton at the position of electron is:

b) The resultant force on the electron is:

c) Let be the mass of the electron and be its accelaration.So,

d) This same force F is responsible for the circular centripetal motion of the electron.Let be the electron velocity as it orbits the atom.

genius_generous answered 2 years ago

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