Question

For each of the questions, four choices have been provided. Select the correct alternative. The azimuthal quantum number of an electron is zero, then the shape of its orbital will be (a) circular (b) spherical (c) elliptical (d) dumbbell

Short answer

Answer: (b) spherical

Step-by-step solution

Recall the meaning of azimuthal quantum number (l)

The azimuthal quantum number (l) determines the shape of the electron's orbital and is related to the angular momentum of electrons in an atom. It can have integer values ranging from 0 to (n-1), where n is the principal quantum number.

Identify the shape of orbitals for l=0

When the azimuthal quantum number (l) is equal to 0, the shape of the orbital is spherical. These orbitals are known as s orbitals. They are non-directional and symmetric around the nucleus.

Choose the correct answer

Based on the above information, when l=0, the shape of the electron's orbital will be spherical. Therefore, the correct answer is (b) spherical.

Key concepts

Quantum Numbers in Chemistry

Quantum numbers are key to understanding the complex workings of electrons within atoms. These numbers provide a set of solutions to the Schrödinger equation, defining the unique quantum state of an electron.
One can liken quartz numbers to an electron's address within an atom. Here, you'll find four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).

• Principal quantum number (n): This number correlates with the size and energy level of the electron's orbit. It's an integer that determines the electron shell.
• Azimuthal quantum number (l): It defines the shape of the orbital and contributes to the angular momentum. This value ranges from 0 to n-1 for each shell.
• Magnetic quantum number (m_l): This number describes the orientation of the orbital in space for a particular subshell, having a value between -l and +l, including zero.
• Spin quantum number (m_s): It describes the direction of the intrinsic spin of the electron, with possible values of +1/2 or -1/2.

Each quantum number plays a pivotal role in detailing the position and energy state of electrons in an atom, which in turn influences everything from chemical bonding to the color of an element.

Orbital Shapes

Moving beyond the numbers, let's focus on the physical interpretation of the azimuthal quantum number ( l) which particularly concerns the shape of electron orbitals. Orbitals can be visualized as the probable regions in space where one is likely to find electrons. As the value of l changes, so does the configuration of these orbitals.
They come in various shapes:

• s Orbitals (l=0): These are spherical and represent a simple 3D region of space around the nucleus where finding an electron is highly probable.
• p Orbitals (l=1): These have a dumbbell shape, with two lobes extending outwards from the nucleus along an axis.
• d Orbitals (l=2): More complex, having mostly cloverleaf shapes with four lobes, or a donut shape with a 'torus' around the middle lobe.
• f Orbitals (l=3): These are even more intricate, with multiple lobes. They rarely come into play except in the chemistry of the actinides and lanthanides.

A concrete understanding of orbital shapes is crucial in predicting and explaining the chemical behavior and reactivity of atoms.

s Orbitals

Let's delve into the spherically symmetrical s orbitals. These orbitals are represented by the azimuthal quantum number ( l) being 0. Regardless of the principal quantum number n, which could be 1, 2, 3, and so on, an s orbital will always appear spherical in shape.
This uniform shape is due to the lack of angular nodes — there's an equal probability of finding an electron at any orientation around the nucleus within the orbital's boundary.
Attributes of s orbitals:

• They always start at the nucleus, indicating that there's a non-zero probability of finding an electron close to the nucleus.
• They are non-directional, meaning they do not preferentially point in any direction, in contrast to p or d orbitals.
• The size and energy of s orbitals increase with the principal quantum number ( n).
• Each shell from n=1 upward has one s orbital, thus we can encounter 1s, 2s, 3s, and so on, each holding up to two electrons.

These characteristics of s orbitals are fundamental in comprehending the electronic structure of atoms and the formation of chemical bonds, such as the single bond in hydrogen molecules.