Among the elements N, O, P, and S, which element or elementshave the smallest effect nuclear charge if we use Equation7.1 to calculate Zeff? Which element or elements havethe largest effective nuclear charge?

Verified step by step guidance

Step 1: Understand the concept of effective nuclear charge (Zeff). It is the net positive charge experienced by an electron in a multi-electron atom. The greater the Zeff, the more strongly the electron is attracted to the nucleus.

Step 2: The effective nuclear charge can be calculated using Slater's rule, which is likely the Equation 7.1 referred to in the question. According to Slater's rule, Zeff = Z - S, where Z is the atomic number and S is the screening constant.

Step 3: The atomic numbers for N, O, P, and S are 7, 8, 15, and 16 respectively. The screening constant S depends on the electron configuration of the atom. For these elements, which are all in the second and third periods of the periodic table, S is approximately equal to the number of inner-shell electrons.

Step 4: For N and O, there are 2 inner-shell electrons, so S = 2. For P and S, there are 10 inner-shell electrons, so S = 10.

Step 5: Therefore, the elements with the smallest Zeff will be those with the smallest Z - S, which are N and O. The elements with the largest Zeff will be those with the largest Z - S, which are P and S.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Effective Nuclear Charge (Zeff)

Effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (the number of protons) minus the shielding effect of other electrons. This concept is crucial for understanding how strongly electrons are attracted to the nucleus, influencing atomic size and ionization energy.

Shielding Effect

The shielding effect refers to the phenomenon where inner-shell electrons partially block the attraction between the nucleus and the outer-shell electrons. This results in a lower effective nuclear charge felt by the outer electrons. Understanding this concept is essential for calculating Zeff, as it helps explain variations in atomic properties across different elements.

Trends in the Periodic Table

Trends in the periodic table, such as atomic size, ionization energy, and electronegativity, are influenced by effective nuclear charge. Generally, as you move across a period from left to right, Zeff increases due to the addition of protons without a corresponding increase in shielding. Conversely, moving down a group increases shielding, which can affect the effective nuclear charge experienced by outer electrons.

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Textbook Question

The prefix eka- comes from the Sanskrit word for 'one.' Mendeleev used this prefix to indicate that the unknown element was one place away from the known element that followed the prefix. For example, eka-silicon, which we now call germanium, is one element below silicon. Mendeleev also predicted the existence of eka-manganese, which was not experimentally confirmed until 1937 because this element is radioactive and does not occur in nature. Based on the periodic table shown in Figure 7.1, what do we now call the element Mendeleev called eka-manganese?

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Textbook Question

Which of the following statements about effective nuclear charge for the outermost valence electron of an atom is incorrect? (i) The effective nuclear charge can be thought of as the true nuclear charge minus a screening constant due to the other electrons in the atom. (ii) Effective nuclear charge increases going left to right across a row of the periodic table. (iii) Valence electrons screen the nuclear charge more effectively than do core electrons. (iv) The effective nuclear charge shows a sudden decrease when we go from the end of one row to the beginning of the next row of the periodic table. (v) The change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table

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Textbook Question

Detailed calculations show that the value of Zeff for the outermost electrons in Na and K atoms is 2.51+ and 3.49+, respectively. (a) What value do you estimate for Zeff experienced by the outermost electron in both Na and K by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

Textbook Question

Detailed calculations show that the value of Zeff for the outermost electrons in Na and K atoms is 2.51+ and 3.49+, respectively. (b) What values do you estimate for Zeff using Slater’s rules?