Question

Write the ground-state electron configuration of radium (Ra), using both the full notation and the noble gas abbreviated notation.

Short answer

The ground-state electron configuration of radium (Ra) is: Full notation: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 \) Noble gas abbreviated notation: \( [Rn] 7s^2 \)

Step-by-step solution

Determine the number of electrons for a neutral radium atom

Radium (Ra) is an alkaline earth metal, and its atomic number is 88. In a neutral atom, the number of electrons is equal to the atomic number. Thus, there are 88 electrons in a neutral radium atom.

Distribute electrons among atomic orbitals using the aufbau principle

By following the aufbau principle, which states that electrons fill orbitals in the order of increasing energy levels, we distribute the 88 electrons in radium as follows: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s² So, the full electron configuration of radium is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s²

Find the noble gas before radium

Radon (Rn) is the noble gas that comes directly before radium (Ra) in the periodic table. Its atomic number is 86. So, the electron configuration of radon is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶

Write the noble gas abbreviated notation

We can now replace the electron configuration of radon (Rn) in the full electron configuration of radium (Ra) to obtain the noble gas abbreviated notation for radium: \[ [Rn] 7s^2 \] Thus, the ground-state electron configuration of radium (Ra) is: Full notation: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 \) Noble gas abbreviated notation: \( [Rn] 7s^2 \)

Key concepts

Radium

Radium is a chemical element with the symbol Ra and atomic number 88. It is classified as an alkaline earth metal, which is found in Group 2 of the periodic table. Radium is highly radioactive and was discovered by Marie Curie and her husband Pierre Curie in 1898. Although radium is luminous and was once used in watch dials, its radioactivity makes it hazardous.

Radium is relatively rare in the Earth’s crust and mostly occurs in uranium and thorium ores. One of its most notable characteristics is its ability to emit alpha particles, a type of ionizing radiation. Because it is radioactive, handling radium requires strict safety precautions.

Aufbau Principle

The aufbau principle is a guideline used to determine the electron configuration of an atom, specifically how electrons are distributed among various orbitals. It is essential for understanding the structure of atoms and predicting chemical behavior.

The principle follows these basic rules:

• Electrons fill orbitals starting with the lowest energy level available.
• Each orbital can hold a maximum of two electrons with opposite spins, known as the Pauli exclusion principle.
• Before pairing up in an orbital, electrons will fill separate orbitals within the same subshell (Hund's rule).

Applying the aufbau principle allows us to derive the electron configuration of elements like radium, ensuring electrons are assigned their lowest possible energy states initially, thereby maintaining stability.

Noble Gas Notation

The noble gas notation is a shorthand way of writing electron configurations, making them more manageable, especially for larger atoms like radium. Instead of writing out every single orbital, chemists use the configuration of the nearest noble gas with fewer electrons as a starting point.

Noble gases, located in Group 18 of the periodic table, have complete electron shells, making them stable. For radium, the noble gas preceding it is radon (Rn), which has an atomic number of 86. This allows us to abbreviate radium's electron configuration, simplifying it to include only the electrons added after radon: \[ [Rn] 7s^2 \] This method highlights the additional electrons in new orbitals, providing a clear picture of valence electrons.

Electron Orbitals

Electron orbitals are regions around an atom’s nucleus where electrons are most likely to be found. They are categorized by energy levels and sublevels, denoted as 's', 'p', 'd', and 'f'. These orbitals have different shapes and capacities:

• s orbitals are spherical, holding up to 2 electrons.
• p orbitals are dumbbell-shaped and can hold up to 6 electrons.
• d orbitals have a more complex shape, accommodating up to 10 electrons.
• f orbitals, even more complex, can store up to 14 electrons.

For radium, these orbitals fill sequentially following the aufbau principle, resulting in an electron configuration that ends with the 7s orbital. Understanding these orbitals helps delineate not only the electron configuration but also an atom's chemical properties and behavior.