One method for calculating Zeff is to use the equation

Question

where E is the energy necessary to remove an electron from an atom and n is the principal quantum number of the elec-tron. Use this equation to calculate Zeff values for the highest-energy electrons in potassium (E = 418.8 kJ/mol) and krypton (E = 1350.7 kJ/mol).

Accepted Answer

Welcome back everyone. An alternate formula for effective nuclear charge is given as follows. Where E. Is the ionization energy of the neutral atom and as the principal quantum number of the highest energy electron, we need to calculate effective nuclear charge for magnesium given its ionization energy of 7 37.7 kg per mole. And florian's ionization energy of 1681. kg per mole. Using the above formula. So we're going to begin with first magnesium Where we want to recognize that on our periodic table. Magnesium is located in group two a across period three. And because it lies across period three, we would assign it a principal quantum number represented by N equal to three since it's at the third energy level. So for our effective nuclear charge calculation for magnesium, We would say that we have the square root so it's equal to the square root of magnesium ionization energy given in the prompt as 737.7 kg jewels Permal. Which is Multiplied by the principle quantum number of three squared And then divided by 1,312 killer jewels per mole. And so simplifying everything, we're going to cancel out our units of kilograms per mole and be left with no units for effective nuclear charge since it's just a magnitude. And when we carefully type this into our calculators, we're going to yield an effective nuclear charge of 2.254 hour magnesium. This would be our first answer. And or sorry our first answer as the effective nuclear charge of magnesium here and now we want to follow the same process. But for our second atom being florian mentioned in the prompt, where for flooring we want to recognize on our periodic table, it's located in group seven A. And lies across period two. And because it lies across period two, we would assign it a principal quantum number equal to two, so N. Is equal to two here. And for our affected nuclear charge calculation for flooring we're going to take the square root of its ionization energy given in the prompt as 1681 point oh killer joules per mole. Which is multiplied by the principal quantum number which we determined to be two squared and divided by 1312 kg jewels per mole. And so canceling out our units of joules per mole. We're left with no units and we're going to yield an effective nuclear charge of 2.26. And this would be our second final answer. Making up our affected nuclear charges of our two atoms magnesium and flooring. So I hope that everything I explained was clear. If you have any questions, please leave them down below. And I'll see everyone in the next practice video

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