A set of seven species

CHEMISTRY · Multi-part · AP · Chemistry · Atomic Structure and Properties · Atomic Structure and Properties

Problem

A set of seven species, each with eighteen electrons, is listed below along with measured or tabulated radii. One of the species is an unidentified cation

X^{n+}

Species	Nuclear Charge, Z	Measured Radius (pm)
$P^{3-}$	15	212
$S^{2-}$	16	184
$Cl^{-}$	17	181
Ar	18	71
$K^{+}$	19	138
$Ca^{2+}$	20	100
$X^{n+}$	?	75

Assume all particles are in the gas phase and do not interact with one another. (1) Part 1: (a) Analyze the numerical data and describe the overall trend in radius as the nuclear charge increases from

Z = 15

Z = 20

. Support your description with one quantitative observation drawn from the table. (2) Part 2: (b) Using the measured radius of

75\,\text{pm}

for

X^{n+}

, determine the most probable atomic number and charge of the unidentified ion. Clearly outline the steps in your reasoning. (3) Part 3: (c) Explain, on the basis of fundamental atomic properties, why adding protons to the nucleus while the electron count remains unchanged leads to the trend you identified in part (a).

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