Identify the following elements based on their electron configurations and rank them in order of increasing electronegativity: $[\operatorname{Ar}] 4 s^{1} 3 d^{5} ;[\mathrm{Ne}] 3 s^{2} 3 p^{3} ;[\operatorname{Ar}] 4 s^{2} 3 d^{10} 4 p^{3} ;[\mathrm{Ne}] 3 s^{2} 3 p^{5}$

First, let's identify the elements by using their electron configuration. We can do this using the periodic table by noting the number of electrons in each subshell of the given configurations. 1. \([\operatorname{Ar}] 4s^1 3d^5\): Argon has 18 electrons, and \([Ar]\) represents the first 18 electrons in their respective subshells. The eleventh electron in this case resides in the 4s orbital, and then there are five more electrons in the 3d orbital. So, the total electron count becomes \(18 + 1 + 5 = 24\), which corresponds to the element Chromium (Cr). 2. \([\mathrm{Ne}] 3s^2 3p^3\): Neon has 10 electrons, and \([Ne]\) represents the first 10 electrons in their respective subshells. Two more electrons are included in the 3s orbital, and three more electrons in the 3p orbital. Thus, the total electron count becomes \(10 + 2 + 3 = 15\), representing Phosphorus (P). 3. \([\operatorname{Ar}] 4s^2 3d^{10} 4p^3\): Argon has 18 electrons, followed by two more in the 4s orbital, 10 more in 3d, and three more in the 4p orbital. This totals up to \(18 + 2 + 10 + 3 = 33\), which corresponds to Arsenic (As). 4. \([\mathrm{Ne}] 3s^2 3p^5\): Neon has 10 electrons, followed by two more in the 3s orbital and five in the 3p orbital. Total electron count is \(10 + 2 + 5 = 17\), which represents the element Chlorine (Cl).

Electronegativity is the measure of the ability of an atom to attract electrons. In general, electronegativity increases from left to right across a period and decreases as you go down a group in the periodic table. Therefore, we can use trend properties to compare the electronegativity of these identified elements.

Based on the periodic trends for electronegativity, let's rank the identified elements: - Chromium (Cr) is a transition metal, and transition metals typically have lower electronegativities compared to non-metals such as P, As, and Cl. - Phosphorus (P) and Arsenic (As) are in the same group (Group 15), with Phosphorus above Arsenic. Since electronegativity decreases as you go down a group, P is more electronegative than As. - Chlorine (Cl) is on the right of Phosphorus (P) in the periodic table, and electronegativity increases as you move from left to right across a period. Therefore, Cl is more electronegative than P. Considering these trends, the order of the increasing electronegativity for the identified elements is: Chromium (Cr) < Arsenic (As) < Phosphorus (P) < Chlorine (Cl)