Question

Into how many sublevels is the third principal energy level of hydrogen divided? What are the names of the orbitals that constitute these sublevels? What are the general shapes of these orbitals?

Short answer

The third principal energy level of hydrogen is divided into 3 sublevels: 3s, 3p, and 3d. The 3s orbital is spherical, the 3p orbitals are dumbbell-shaped, and the 3d orbitals have mainly two shapes: four four-leaf clover-shaped orbitals, and one with a dumbbell shape and a donut-shaped ring around its center.

Step-by-step solution

Determine the number of sublevels in the third energy level

The number of sublevels in an energy level is determined by the principal quantum number n. The number of sublevels in an energy level is equal to the value of n. In this case, the third principal energy level (n=3) has 3 sublevels.

Identify the orbitals in each sublevel

In every sublevel, there are different types of orbitals. The orbitals are labeled by the angular momentum quantum number (l), and l can have integral values from 0 to (n-1). Each orbital has a specific name associated with it: - l=0 is called the 's' orbital - l=1 is called the 'p' orbital - l=2 is called the 'd' orbital In the third energy level (n=3), there will be three sublevels with the following values of l: 1. l=0 (s orbital) 2. l=1 (p orbital) 3. l=2 (d orbital) Thus, the sublevels in the third principal energy level are 3s, 3p, and 3d.

Describe the general shapes of the orbitals

The general shapes of the orbitals are as follows: 1. s Orbital: The s orbitals are spherical in shape, centered on the nucleus. All s orbitals, regardless of the energy level, have this general shape. So the 3s orbital will be spherical as well. 2. p Orbital: The p orbitals have a dumbbell shape, with two lobes on either side of the nucleus. There are three p orbitals in a sublevel with l=1, corresponding to the three possible values of the magnetic quantum number (m_l). These are labeled as p_x, p_y, and p_z, indicating their orientation along the x, y, and z axes, respectively. Therefore, the 3p orbitals will follow this general shape. 3. d Orbital: The d orbitals have mainly two types of shapes: four of them are in the form of a four-leaf clover, and one has a dumbbell shape with a donut-shaped ring around its center. There are five d orbitals in a sublevel with l=2 due to the five possible values of the magnetic quantum number (m_l). Thus, the 3d orbitals will have these general shapes. In conclusion, the third principal energy level of hydrogen is divided into 3 sublevels: 3s, 3p, and 3d. The 3s orbital is spherical, the 3p orbitals are dumbbell-shaped, and the 3d orbitals have mainly two shapes: four four-leaf clover-shaped orbitals, and one with a dumbbell shape and a donut-shaped ring around its center.

Key concepts

Principal Quantum Number

The principal quantum number, denoted as \( n \), is fundamental in quantum mechanics as it represents the primary energy level of an electron in an atom. It provides insight into the electron's energy and helps categorize the probability zones that the electron may occupy. For hydrogen, since it's a simple atom with only one electron, these energy levels are all summed up in \( n \).

• Each energy level is specific to the principal quantum number.
• The value of \( n \) starts from 1 (closest to the nucleus) and increases to the outer regions.
• The level number determines the number of sublevels, meaning if \( n = 3 \), there are 3 sublevels.

To put it simply, understanding the principal quantum number gives clarity to the distribution and energy of electrons around the nucleus, especially in a simplistic atom like hydrogen, where these principles become very evident.

Orbital Shapes

Orbitals are regions in an atom where there is a high probability of finding an electron. Each orbital is associated with a specific shape, which is dictated by the different angular momentum quantum numbers \( l \). The shapes play a key role in chemical bonding and properties.

• s Orbital: Always spherical, meaning electrons can be found in regions equally around the nucleus, like a fuzzy ball.
• p Orbital: Shaped like a dumbbell, these orbitals have directional characteristics and can be aligned along x, y, or z axes.
• d Orbital: More complex, with four displaying a cloverleaf shape and one resembling a donut surrounding a dumbbell. These appear in higher energy levels.

Hydrogen's orbitals each possess these distinct shapes, reflecting quite straightforward geometry when examining low-energy situations, which becomes more intricate as energy levels increase.

Hydrogen Atom

The hydrogen atom is the simplest atom, consisting of one proton and one electron. It's an ideal model for studying quantum mechanics since it sets the foundational understanding of other, more complex atoms.

• The simplicity of hydrogen makes its behavior more predictable, and its energy levels easy to calculate using quantum mechanics.
• Hydrogen's spectrum provides key insights into quantum mechanics as its electronic transitions produce well-defined spectral lines.
• The distinct formation of its orbitals establishes the basics for understanding more complex atoms, basically acting as a building block for more sophisticated atomic theory.

In hydrogen, the third principal energy level's sublevels (3s, 3p, and 3d) articulate the elegant simplicity and precision of quantum mechanical models, making it a pivotal topic for anyone delving into the basics of quantum mechanics.