Question

When a hydrogen atom is in its ground state, in which orbital is its electron found? Why?

Short answer

In the ground state of a hydrogen atom, the electron is found in the 1s orbital. This is because the 1s orbital has the lowest energy, which stabilizes the hydrogen atom. The strong electrostatic attraction between the proton and electron when the electron is in the 1s orbital contributes to this stability.

Step-by-step solution

Understand the structure of a hydrogen atom

A hydrogen atom consists of a single proton in its nucleus and one electron revolving around the nucleus. In quantum mechanics, the position of the electron around the nucleus is described by orbitals.

Concept of orbitals and quantum numbers

Orbitals are regions in space where an electron is most likely to be found. They are defined by a combination of quantum numbers, namely the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m_l). These quantum numbers define the energy, shape, and orientation of the orbitals, respectively. For hydrogen atom: - Principal quantum number (n) represents the energy level and can have positive integers values (1, 2, 3, ...). - Azimuthal quantum number (l) represents the shape of the orbital and can have integer values from 0 to n-1, where 0 is s-orbital, 1 is p-orbital, and so on. - Magnetic quantum number (m_l) represents the orientation of the orbital and can have integer values from -l to +l.

Ground state of a hydrogen atom

The ground state refers to the lowest energy state of an atom, with the electron occupying the lowest possible energy orbital. In the case of a hydrogen atom, the ground state is when the electron occupies the lowest energy level n=1 (first energy shell).

Identify the orbital for hydrogen atom's ground state

According to the quantum numbers, we can find the orbital for hydrogen atom's ground state: - Since n=1 (as explained in step 3), the azimuthal quantum number (l) can only be 0 (values range from 0 to n-1). - In this case, the magnetic quantum number (m_l) can only be 0, as it ranges from -l to +l. With these quantum numbers, we can determine that the electron in a hydrogen atom's ground state is found in the 1s orbital.

Reason for the electron in the 1s orbital in the ground state

The electron occupies the 1s orbital in the ground state because it is the orbital with the lowest energy, which stabilizes the hydrogen atom. Due to its lower energy, the electron is most likely to be found closer to the nucleus, creating a strong electrostatic attraction between the positively charged proton and the negatively charged electron. This attraction results in the hydrogen atom being most stable when its electron is in the 1s orbital.

Key concepts

Ground State

The ground state of an atom is its most stable and lowest energy state. When thinking about the hydrogen atom, it mainly consists of one proton and one electron. The ground state is vital because it represents the electron's most stable position. The electron seeks to be in this state due to lower energy requirements, which ensures stability.

The hydrogen atom's electron, in its ground state, is found in the lowest energy level, which is the first energy shell (n=1). This is the basic level for electrons, as higher energy levels are only occupied if additional energy is provided. The electron naturally falls back to this ground state to reduce the atom's overall energy.

This is crucial in understanding atomic behavior because in their ground states, atoms are most efficiently configured, providing insight into reactions and interactions at a quantum level. Understanding why electrons occupy certain states helps in chemistry and physics to predict and manipulate atomic behavior.

Quantum Numbers

Quantum numbers are like the unique address for an electron in an atom. They help to describe the electron's position in terms of energy level, orbital shape, and orientation. Let's break these down one by one:

• Principal Quantum Number ( ext{n} ): This number indicates the energy level of an electron. It's always a positive integer (1, 2, 3,...). In hydrogen's ground state, ext{n=1} since the electron occupies the innermost energy level.
• Azimuthal Quantum Number ( ext{l} ): This defines the shape of the orbital that the electron occupies. Depending on ext{n} , ext{l} can take values from 0 to ext{n-1} . For n=1, l can only be 0, corresponding to an 's' orbital.
• Magnetic Quantum Number ( ext{m}_l ): This number specifies the orientation of the orbital in space. Its range is from -l o+l . When ext{l=0} , ext{m}_l is also 0.

Understanding these quantum numbers allows us to describe the electron configuration precisely. It's like understanding a map with latitude, longitude, and altitude to define a specific location. Each electron in an atom has a unique set of these numbers, ensuring no two electrons in the same atom have the exact same set of quantum numbers due to the Pauli exclusion principle.

Orbitals

Orbitals can be thought of as cloud-like regions where the electron is most likely to be found. These are not fixed paths but regions shaped by the wave-like nature of electrons, dictated by quantum mechanics.

When discussing hydrogen, in its simplest form, the electron is located in the 1s orbital, which is spherical. This orbital encompasses the area around the nucleus where finding the electron is statistically most likely.

Orbitals are determined by the quantum numbers we discussed earlier. The combination of these numbers indicates not just the likelihood of finding an electron in a region, but the very nature and volume of that region.

In the hydrogen atom, the 1s orbital is the only orbital occupied in the ground state. This is because the 1s orbital represents the lowest energy level, which is essential for stability. Understanding orbitals helps in visualizing how atoms bond, react, and interact with one another. They provide the framework upon which much of atomic chemistry is built.