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Chapter 2: Problem 111

In each of the following sets, which atom or ion has the smallest radius? a. \(\mathrm{H}, \mathrm{He}\) b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\) c. element \(120,\) element \(119,\) element 116 d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\) e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

Short Answer

Expert verified
The smallest atomic radii in each set are: a. \(\mathrm{He}\), b. \(\mathrm{Cl}\), c. element \(116\), d. \(\mathrm{Si}\), and e. \(\mathrm{Na}^{+}\).

Step by step solution

01

Identify the trend in the periodic table

Since hydrogen and helium are in the same period (Period 1), we know that the atomic size will decrease when moving across this period. In this case, helium will have a smaller atomic radius than hydrogen.
02

Determine the smallest radius

Since helium has the smallest atomic radius according to the periodic trend, the smallest radius in the set belongs to \(\mathrm{He}\). b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\)
03

Identify the trend in the periodic table

Chlorine, indium, and selenium are all in different groups and periods. Therefore, we must compare their group and period trends. - Chlorine (Group 17, Period 3) - Indium (Group 13, Period 5) - Selenium (Group 16, Period 4) According to the trends, atomic size increases down a group (therefore, indium is larger than chlorine) and atomic size decreases across a period (selenium is smaller than indium).
04

Determine the smallest radius

Based on the trends, chlorine has the smallest atomic radius in the set. c. element \(120,\) element \(119,\) element \(116\)
05

Identify the trend in the periodic table

The elements are in the same period (period 7), so atomic size decreases across the period. Element 116 has the highest atomic number in the period, therefore, it has the smallest atomic radius. d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\)
06

Identify the trend in the periodic table

Niobium, zinc, and silicon are in different periods and groups. Compare their group and period trends: - Niobium (Group 5, Period 5) - Zinc (Group 12, Period 4) - Silicon (Group 14, Period 3) Atomic size increases down a group and decreases across a period.
07

Determine the smallest radius

Based on the trends, silicon has the smallest atomic radius in the set. e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)
08

Determine the effect of charge on atomic radius

Cations (positive charges) have smaller atomic radii while anions (negative charges) have larger atomic radii. In this set of ions, the \(\mathrm{Na}^{-}\) ion has a negative charge, making its atomic radius larger, and the \(\mathrm{Na}^{+}\) ion has a positive charge, making its atomic radius smaller.
09

Determine the smallest radius

In the set, \(\mathrm{Na}^{+}\) has the smallest atomic radius due to its positive charge.

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Most popular questions from this chapter

As the weapons officer aboard the Starship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is \(7.52 \times 10^{-19} \mathrm{J}\) a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of \(259 \mathrm{nm}\) and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configuration of \([\mathrm{Ar}] 4 s^{1} 3 d^{10},\) what metal is this?

Write equations corresponding to the following: a. the fourth ionization energy of Se b. the electron affinity of \(S^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)

Identify the following three elements. a. The ground-state electron configuration is \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\). b. The ground-state electron configuration is \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{2}\). c. An excited state of this element has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\).

The ionization energy for a \(1 s\) electron in a silver atom is \(2.462 \times 10^{6} \mathrm{kJ} / \mathrm{mol}\) a. Determine an approximate value for \(Z_{\text {eff }}\) for the Ag \(1 s\) electron. Assume the Bohr model applies to the 1 s electron. \(Z_{\mathrm{eff}}\) is the apparent nuclear charge experienced by the electrons. b. How does \(Z_{\text {eff }}\) from part a compare to \(Z\) for Ag? Rationalize the relative numbers.

In each of the following sets, which atom or ion has the smallest ionization energy? a. \(\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{K}, \mathrm{Mn}, \mathrm{Ga}\) c. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) d. \(S^{2-}, S, S^{2+}\) e. \(\mathrm{Cs}, \mathrm{Ge}, \mathrm{Ar}\)
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