Question

Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) \(\mathrm{Br}\), (b) Ga, (c) Hf, (d) Sb, (e) Bi, (f) Sg.

Short answer

(a) Br: \[ [Ar] 4s^2 3d^{10} 4p^5 \], 1 unpaired electron (b) Ga: \[ [Ar] 4s^2 3d^{10} 4p^1 \], 1 unpaired electron (c) Hf: \[ [Xe] 6s^2 4f^{14} 5d^2 \], 2 unpaired electrons (d) Sb: \[ [Kr] 5s^2 4d^{10} 5p^3 \], 3 unpaired electrons (e) Bi: \[ [Xe] 6s^2 4f^{14} 5d^{10} 6p^3 \], 3 unpaired electrons (f) Sg: \[ [Rn] 7s^2 5f^{14} 6d^4 \], 4 unpaired electrons

Step-by-step solution

(a) Br - Electron Configuration and Unpaired Electrons

First, let's find bromine (Br) in the periodic table. It is in group 7 and period 4, with an atomic number of 35. To write the electron configuration, go through the periodic table starting from Hydrogen (H) and counting up to Br, which will give the order of filling electron orbitals: Br: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^5\] The condensed electron configuration is: Br: \[ [Ar]4s^2 3d^{10} 4p^5 \] The number of unpaired electrons in the ground state of Br can be found by looking at its final orbital (4p) which has 5 electrons. Since a p orbital can hold 6 electrons, we can determine that there is one unpaired electron.

(b) Ga - Electron Configuration and Unpaired Electrons

Next, let's locate gallium (Ga) in the periodic table. It is in group 13 and period 4, with an atomic number of 31. Following the same steps as before: Ga: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^1\] The condensed electron configuration is: Ga: \[ [Ar] 4s^2 3d^{10} 4p^1 \] Ga has one electron in its 4p orbital, which means it has one unpaired electron.

(c) Hf - Electron Configuration and Unpaired Electrons

Now, let's find hafnium (Hf) in the periodic table. It is in group 4 and period 6, with an atomic number of 72. The electron configuration will be: Hf: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^6, 6s^2, 4f^{14}, 5d^2 \] The condensed electron configuration is: Hf: \[ [Xe] 6s^2 4f^{14} 5d^2 \] Hf has two electrons in its 5d orbital, which means it has two unpaired electrons.

(d) Sb - Electron Configuration and Unpaired Electrons

Next, let's find antimony (Sb) in the periodic table. It is in group 15 and period 5, with an atomic number of 51. Write its electron configuration: Sb: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^3\] The condensed electron configuration is: Sb: \[ [Kr] 5s^2 4d^{10} 5p^3 \] Sb has three electrons in its 5p orbital, which means it has three unpaired electrons.

(e) Bi - Electron Configuration and Unpaired Electrons

Now, let's find bismuth (Bi) in the periodic table. It is in group 15 and period 6, with an atomic number of 83. Write its electron configuration: Bi: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^6, 6s^2, 4f^{14}, 5d^{10}, 6p^3\] The condensed electron configuration is: Bi: \[ [Xe] 6s^2 4f^{14} 5d^{10} 6p^3 \] Bi has three electrons in its 6p orbital, which means it has three unpaired electrons.

(f) Sg - Electron Configuration and Unpaired Electrons

Finally, let's find seaborgium (Sg) in the periodic table. It is in group 6 and period 7, with an atomic number of 106. Write its electron configuration: Sg: \[1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^6, 6s^2, 4f^{14}, 5d^{10}, 6p^6, 7s^2, 5f^{14}, 6d^4\] The condensed electron configuration is: Sg: \[ [Rn] 7s^2 5f^{14} 6d^4 \] Sg has four electrons in its 6d orbital, which means it has four unpaired electrons.

Key concepts

Periodic Table

The periodic table is a powerful tool in chemistry that organizes all known elements in a systematic way. Elements are arranged in increasing order based on atomic number, which is the number of protons an element has in its nucleus. This arrangement reveals patterns in the properties of elements. These patterns are called

• groups (vertical columns),
• periods (horizontal rows).

Each element's position in the periodic table helps predict its electron configuration. Electron configuration refers to the distribution of electrons in an atom's atomic orbitals. Understanding the periodic table allows us to determine how many electrons are in each energy level, and subsequently, how they are arranged within sublevels (like s, p, d, and f), which each accommodate a specific number of electrons.
Furthermore, the periodic table can show which orbitals are being filled across different periods, helping us deduce properties related to atomic size, ionization energy, and electron affinity.

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where electrons are most likely to be found. They are shaped in various forms (spherical, dumbbell-shaped, etc.) and are labeled as s, p, d, or f depending on their shape. Each type of orbital can hold a specific number of electrons:

• s orbitals can hold up to 2 electrons,
• p orbitals can hold up to 6 electrons,
• d orbitals can hold up to 10 electrons,
• f orbitals can accommodate up to 14 electrons.

Knowing the capacity of each orbital is crucial when determining an element’s electron configuration.
An atom's electron configuration helps us understand how electrons are arranged in these orbitals, starting from the lowest energy level to the higher ones. This arrangement follows the Aufbau principle, where electrons fill orbitals from lowest to highest energy levels. The periodic table helps predict the order in which orbitals are filled.

Unpaired Electrons

Unpaired electrons are electrons that occupy an atomic orbital on their own, without pairing with another electron. These unpaired electrons are vitally important in chemistry because they contribute to an atom's magnetic properties and its chemical reactivity.
In the context of electron configuration, observing unpaired electrons can be crucial for understanding the behavior of molecules in reactions. Each orbital should ideally host paired electrons which spin in opposite directions; unpaired electrons imply there are odd numbers of electrons in those particular orbitals.
For instance, in the electron configuration of bromine, which ends in 4p^5, one electron remains unpaired because the p orbital can hold up to six electrons, meaning one electron does not have a pair. Such unpaired electrons are prime contributors to the reactivity and bonding patterns observed in elements.