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Which substance in each of the following pairs has the larger lattice energy?

Which substance in each of the following pairs has the larger lattice energy?

A.)  KCl or RbCl

B.)  CaF2 or BaF2

C.)  CaO or KI

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Effective Nuclear Charge and Ionization Energy

Effective nuclear charge, Zeff, is defined as


where Z is true nuclear charge and S is the amount of shielding.

In 1930, John C. Slater devised the following set of empirical rules to estimate S for a designated ns or np electron:

  1. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4), (5s, 5p), and so on.
  2. Electrons in groups to the right of the (ns, np) group contribute nothing to the shielding constant for the designated electron.
  3. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each.
  4. All electrons in the n−1 shell shield to the extent of 0.85 each.
  5. All electrons in the n−2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each.

When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following:

  1. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant.

These rules are a simplified generalization based on the average behavior of different types of electrons.

A.)  Calculate Z eff for a valence electron in an oxygen atom

B.)  Calculate Z eff for the 4s electron in a copper atom, Cu.

C.)  Calculate Z eff for a 3d electron in a copper atom, Cu.



Ionic Radii

The size of ions as measured by ionic radii varies in a systematic manner. The size of the ion can be explained in part by effective nuclear charge, Z eff, which is the net nuclear charge felt by an electron. The effective nuclear charge takes into account the actual nuclear charge and the shielding of this charge by inner electrons. When an atom loses electrons, the resulting cation is smaller both because the remaining electrons experience a larger Z eff and because these electrons are usually in orbitals closer to the nucleus than the electrons that were lost. The more electrons that are lost, the smaller the ion becomes.

Similarly, when an atom gains electrons, the resulting anion is larger owing to both increased electron-electron repulsions and a reduction in Z eff. The more electrons that are gained, the larger the ion becomes.

1.)  Rank the following ions in order of decreasing radius: F− , Cl− , Br− , I− , and At− .

2.)  Rank the following items in order of decreasing radius: Ca , Ca2+ , and Ca2− .

3.)  Rank the following in order of decreasing ionic radii.  K+, S^2-, Ca^2+, Sc^3+, Cl^-, P^3-

Analysis of Metallic Oxides

Metals often react with oxygen to produce ionic oxides such as K2O, CaO, TiO2, and V2O5.

Give the oxidation state for the metal ion in each of the following compounds.

K2O, CaO, TiO2, V2O5

Zinc Emission Spectrum

Which of the following are valid transitions?

During an emission, electrons move from a higher energy orbital to a lower energy orbital. Which of the following are valid transitions that produce lines in the emission spectrum of Zn?

1.)  [Ar] 3d10→[Ar] 4s2, 3d10

2.)  [Ar] 4s2, 3d10→[Ar] 4s1, 3d11

3.)  [Ar] 4s2, 3d10→[Ar] 3d10

4.)  [Ar] 4s1, 3d10, 6s1→[Ar] 4s2, 3d10

5.)  [Ar] 4s2, 3d10→[Ar] 4s1, 3d10, 6s1     

6.)  [Ar] 4s2, 3d10→[Ar] 4s2, 3d10, 4p2

Electron Configurations of Atoms

An atom consists of a small, positively charged nucleus, surrounded by negatively charged electrons. We organize the electrons in a logical manner. As the atomic number increases, electrons are added to the subshells according to their energy. Lower energy subshells fill before higher energy subshells.

The order of filling is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

The periodic table can be used to help you remember the order.

Give the complete ground-state electron configuration for silicon

Give the ground-state electron configuration for silicon (Si) using noble-gas shorthand.

Give the actual ground-state electron configuration for copper (Cu) using the complete form.

Give the ground-state electron configuration for copper (Cu) using noble-gas shorthand.

Quantum Number Rules

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.

The principal quantum number n corresponds to the shell in which the electron is located. Thus n can therefore be any integer. For example, an electron in the 2p subshell has a principal quantum number of n=2 because 2p is in the second shell.

The azimuthal or angular momentum quantum number ℓ corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and f as 3. For example, an electron in the 2p subshell has ℓ=1. As a rule, ℓ can have integer values ranging from 0 to n−1.

The magnetic quantum number mℓcorresponds to the orbital in which the electron is located. Instead of 2px, 2py, and 2pz, the three 2p orbitals can be labeled −1, 0, and 1, but not necessarily respectively. As a rule, mℓcan have integer values ranging from −ℓ to +ℓ.

The spin quantum number ms corresponds to the spin of the electron in the orbital.  A value of 1/2 means an “up” spin, whereas −1/2means a “down” spin.

What is the only possible value of mℓ for an electron in an orbital?

What are the possible values of mℓ for an electron in a d orbital?




Atomic Radii and Effective Nuclear Charge

The atomic radius of an element can be predicted based on its periodic properties. Atomic radii increase going down a group in the periodic table, because successively larger valence-shell orbitals are occupied by electrons. Atomic radii generally decrease moving from left to right across a period because the effective nuclear charge increases.

1.)  Rank Ca Mg Be Sr, from largest to smallest according to their atomic radius.

2.)  Rank Li, Be, B, N, from largest to smallest according to their atomic radius.

Molar Volume of Sodium

You can estimate the average volume of space it occupies using basic geometry.

Estimate the volume, V, of one sodium atom (Na) using its metallic radius of 186  pm.

Zinc Emission Spectrum

Scientists can analyze metals using the emission spectrum produced when the sample is introduced into the flame of an emission spectrometer. The flame provides the energy to excite the electrons of the metal atoms to higher energy states. When the electrons return to the ground state, lines of characteristic wavelengths are produced. The lines in the emission spectrum are characteristic of the metal because each atom’s ground-state electron configuration is unique.

The emission line used for zinc determinations in atomic emission spectroscopy is 214 nm. If there are 8.50×1010atoms of zinc emitting light in the instrument flame at any given instant, what energy (in joules) must the flame continuously supply to achieve this level of emission?


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