Question

For each of the following elements, indicate which set of orbitals is filled last. a. chromium, \(Z=24\) b. silver, \(Z=47\) c. uranium, \(Z=92\) d. germanium, \(Z=32\)

Short answer

For the following elements, the set of orbitals filled last: a. Chromium (Z=24): 3d b. Silver (Z=47): 4d c. Uranium (Z=92): 6d d. Germanium (Z=32): 4p

Step-by-step solution

Recognize the Periodic Table Layout

Remember that the layout of the Periodic Table of Elements is organized according to increasing atomic number (Z) and electron configurations. The periodic table is divided into blocks (s, p, d, and f) based on the type of electron orbitals filled in each element.

Locate the Elements in the Periodic Table

Find the position of each element in the periodic table. This will help you determine the electron configuration and the last set of orbitals filled. a. Chromium (Z = 24) is in the 3d block. b. Silver (Z = 47) is in the 4d block. c. Uranium (Z = 92) is in the 5f block. d. Germanium (Z = 32) is in the 4p block.

Write the Electron Configuration

Use the periodic table to write the electron configuration for each element. a. Chromium (Z = 24): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5\) b. Silver (Z = 47): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10}\) c. Uranium (Z = 92): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^3 6d^1\) d. Germanium (Z = 32): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2\)

Identify the Last Set of Orbitals Filled

Look at the electron configuration and find the last set of orbitals filled for each element. a. Chromium: The last set of orbitals filled is 3d. b. Silver: The last set of orbitals filled is 4d. c. Uranium: The last set of orbitals filled is 6d. d. Germanium: The last set of orbitals filled is 4p. The final answer should include the set of orbitals filled last for each element: a. Chromium: 3d b. Silver: 4d c. Uranium: 6d d. Germanium: 4p

Key concepts

Orbitals

Understanding orbitals is crucial when it comes to determining how electrons are arranged around an atom's nucleus. An orbital is a region of space where there is a high probability of finding an electron. Each orbital can hold a maximum of two electrons. There are four types of orbitals: s, p, d, and f. The s orbital is spherical in shape and each shell starts with it. As we move to higher energy levels, more complex shapes emerge, such as the dumbbell-shaped p orbitals, the clover-shaped d orbitals, and the complex f orbitals.

In a step by step solution of an exercise, identifying the last set of orbitals filled helps us understand an element's reactivity and chemical properties. For instance:

• The 3d orbitals are filled last in chromium, accounting for its unique electron configuration and magnetic properties.
• Silver, with 4d orbitals filled last, reflects its position in the transition metals where d-orbitals play a significant role in bonding and conductivity.

Understanding these configurations requires a grasp of the quantum mechanical model of the atom, where electrons don't orbit the nucleus in neat circles but rather exist in these probabilistic orbitals.

Periodic Table

The periodic table is a comprehensive display of all known chemical elements, organized by increasing atomic number, electron configurations, and recurring chemical properties. The layout is designed to underscore periodic trends, such as elements with similar behaviors falling into the same columns (groups).

Elements are laid out into blocks corresponding to the type of orbital they are filling with electrons – s-, p-, d-, or f-block. When solving problems regarding electron configurations:

• Locating an element on the periodic table immediately suggests the type of orbitals being filled and the configuration pattern.
• Understanding that the rows (periods) represent principal energy levels gives insight into how many shells an atom has.

For an educative and detailed explanation, remind students that the periodic table is not just a reference tool; it's a map of the atomic and chemical structure of matter, explaining why the periodic table is fundamental in chemistry and physics alike.

Atomic Number

The atomic number (Z) of an element is indicative of the number of protons found in the nucleus of an atom, and consequently, the number of electrons that surround the nucleus when the atom is neutral. It's the identity card for elements and a critical concept in chemistry.

This number not only determines an element's position on the periodic table but also its chemical behavior. When providing exercises:

• Highlight that the atomic number allows you to deduce the electron configuration of an atom. For instance, uranium with atomic number 92 means it has 92 electrons to arrange in orbitals.
• Emphasize the predictive power of the atomic number in determining how an element reacts.

The correct order of orbitals being filled according to increasing atomic number is critical when solving for the last set of orbitals filled in an atom, illustrating nuclear charge's influence on the electron cloud's architecture.