work question electrostatics

[pizza1994]

Imagine a lithium atom where the two electrons in the first orbital are at exact opposite sides of the nucelus and the electron in the second orbital is in line with the other electrons so that the three electrons and the nucleus all lie on a straight line. How much work would you need to apply to remove the outermost electron if the atomic radius is 100 pm and teh distance between the first and second orbital is 50 pm?

answer (ke^2/300) * 10^12 J

source is TPR

how do you use the superposition pricneple in this?

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[Ace-Co-A]

The superposition principle refers to the idea that linear systems can be treated as a summation of all interactions between components. In this case, the energy required to oust the outermost electron must be at least the energy associated with the electron's interactions with (1) the two other electrons and (2) the three protons in the Li nucleus. Summing the Coulombic energies of each individual connection (that is, of the electron in question and the two other electrons and three other protons) gives the energy needed to separate the outermost electron from the original atom.

Hope this helps.

 

[pizza1994]

The superposition principle refers to the idea that linear systems can be treated as a summation of all interactions between components. In this case, the energy required to oust the outermost electron must be at least the energy associated with the electron's interactions with (1) the two other electrons and (2) the three protons in the Li nucleus. Summing the Coulombic energies of each individual connection (that is, of the electron in question and the two other electrons and three other protons) gives the energy needed to separate the outermost electron from the original atom.

Hope this helps.

yeah so I get the interaction between the two electrons but why do we also consider the intercation of the 3 protons in the nucleus? Isnt this suppose to be only interactions with electrons orbiting the nucleus??

 

[Ace-Co-A]

yeah so I get the interaction between the two electrons but why do we also consider the intercation of the 3 protons in the nucleus? Isnt this suppose to be only interactions with electrons orbiting the nucleus??

Charged particles interact, and this interaction is described by Coulomb's law. Therefore, in a region of space in which the distance separating them is small (i.e., where R << 1), the Coulombic attraction between a positively charged particle and a negatively-charged particle will be non-negligible when calculating the force necessary to remove the negatively-charged particle from its interaction with the positively charged particle.

Now ask yourself the opposite question that you asked me, 'Why ignore the interaction of charged bodies in your calculation?' There is no answer to this question, and it should show you where you're going wrong. Proceed with your calculation.