Calculating Work Done to Bring Proton to Hydrogen Atom Nucleus

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To calculate the work required to bring a proton to the surface of a hydrogen nucleus, one must determine the change in electric potential as the proton moves from a distance to the nucleus. The nucleus has a radius of 1 x 10^-15 m, and the existing proton creates an electric field that influences the potential energy of the incoming proton. The work done by the external force can be derived from the change in electric potential, which is influenced by Coulomb's law. Careful attention to units and signs is essential in this calculation, as the work done will be expressed in electron volts. Ultimately, the discussion emphasizes the importance of understanding electric potential in relation to work done in atomic physics.
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A hydrogen nucleus has a radius of 1 x 10-15 m and the electron is about 5.4 x 10-11 m from the nucleus. Assume the hydrogen atom is a ball with a radius of about 5.4 x 10-11 m and the nucleus is a ball with a radius of 1 x 10-15 m.

How much work (in electron volts) must be performed by an external force to bring in another proton (from very far away) to the "surface" of the nucleus? (Ignore the effects of the electron.)

HELP: Find the change in electric potential when proton is moved from very far away to the surface of the nucleus (a distance of 1 x 10-15 m from the proton that is already there).

HELP: Now relate this quantity to the work done by the external force. Watch your units and be careful of the sign!
 
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How much work (in electron volts) must be performed by an external force to bring in another proton (from very far away) to the "surface" of the nucleus? (Ignore the effects of the electron.)

HELP: Find the change in electric potential when proton is moved from very far away to the surface of the nucleus (a distance of 1 x 10-15 m from the proton that is already there).

HELP: Now relate this quantity to the work done by the external force. Watch your units and be careful of the sign!
 
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