Question

Which of the following statements is(are) true? a. The \(2 s\) orbital in the hydrogen atom is larger than the \(3 s\) orbital also in the hydrogen atom. b. The Bohr model of the hydrogen atom has been found to be incorrect. c. The hydrogen atom has quantized energy levels. A. An orbital is the same as a Bohr orbit. e. The third energy level has three sublevels, the \(s, p,\) and \(d\) sublevels.

Short answer

Statements b, c, and e are true, while statements a and A are false. The $3s$ orbital is larger than the $2s$ orbital, the Bohr model has been found to be incorrect, hydrogen atoms have quantized energy levels, orbitals are not the same as Bohr orbits, and the third energy level has three sublevels: $s, p,$ and $d$.

Step-by-step solution

Statement a

The \(2s\) orbital in the hydrogen atom is larger than the \(3s\) orbital also in the hydrogen atom. This statement is false. The \(3s\) orbital has a higher principal quantum number, which corresponds to a greater average distance from the nucleus. Therefore, the \(3s\) orbital is larger than the \(2s\) orbital.

Statement b

The Bohr model of the hydrogen atom has been found to be incorrect. This statement is true. While the Bohr model provided some useful insights and predictions about how atomic energy levels are quantized, it doesn't take into account the wave-like properties of electrons nor the Heisenberg Uncertainty Principle. The modern quantum mechanical model provides a more accurate description of atomic structure.

Statement c

The hydrogen atom has quantized energy levels. This statement is true. The energy levels of electrons in a hydrogen atom are quantized, meaning they can only occupy specific, discrete energy levels. This is a fundamental result of quantum mechanics.

Statement A

An orbital is the same as a Bohr orbit. This statement is false. An orbital is a region of space where there is a high probability of finding an electron, described by mathematical functions called wave functions. Bohr orbits are the paths which electrons were thought to move around the nucleus in circles according to the Bohr model, but this concept has been superseded by the quantum mechanical model.

Statement e

The third energy level has three sublevels, the \(s, p,\) and \(d\) sublevels. This statement is true. The third energy level has a principal quantum number \(n = 3\), and it corresponds to having three distinct sublevels: \(s\), \(p\), and \(d\). Each sublevel corresponds to different shapes of the electron orbitals within that energy level. In summary, statements b, c, and e are true, while statements a and A are false.

Key concepts

Quantum Mechanics

Quantum Mechanics is a fundamental theory in physics that describes nature at the smallest scales, such as electrons and photons. It is essential for understanding the behavior of atoms and particles, which classical physics cannot adequately explain.
One of the key aspects of quantum mechanics is that energy levels in atoms are quantized. This means that electrons in an atom can only reside at specific energy levels, rather than being in any arbitrary state.
This characteristic leads to the concept of quantized atomic spectra, where electrons can only gain or lose energy in fixed amounts, corresponding to quantum transitions between energy levels. These quantum mechanics concepts help us understand atomic structures and chemical reactions.

Bohr Model

The Bohr Model was an early 20th-century model proposed to explain the quantization of energy levels in the hydrogen atom. It depicted electrons as moving in fixed circular orbits around the nucleus, similar to planets orbiting the sun.
Despite its historical significance, the Bohr model has limitations, as it doesn't account for electron wave-like behavior or the uncertainty principle.
Although superseded by more advanced quantum mechanical models, the Bohr model was a stepping stone to our current understanding of atomic theory by highlighting energy quantization in atoms.

Energy Levels

Energy levels refer to the specific energies that electrons in an atom possess. They are quantized, meaning electrons can only exist in specific energy states.
Electrons can move between these levels by absorbing or emitting energy, often in the form of light.
Each energy level is associated with a principal quantum number \(n\), which is an integer starting from 1 upwards. The larger the value of \(n\), the further the energy level is from the nucleus. Hence, electrons in higher energy levels have more energy and can travel further from the nucleus.

Orbitals

Orbitals are regions around an atom's nucleus where there is a high probability of finding an electron. Unlike Bohr's orbits, orbitals are not fixed paths. Rather, they are determined by wave functions, which predict an electron's probability distribution.
Orbitals have different shapes, which depend on the type of orbital. The most common types are \(s\), \(p\), \(d\), and \(f\).
The shape of an orbital affects the electron's energy and the way it interacts with other atoms, influencing the chemical properties of the element.

Electron Sublevels

Within each energy level, electrons are further organized into sublevels that represent different orbital shapes and arrangements.
These sublevels are designated by the letters \(s\), \(p\), \(d\), and \(f\), with each having a specific number of orbitals. For example, the \(s\) sublevel has one orbital, the \(p\) has three, the \(d\) has five, and the \(f\) has seven.
The arrangement of electrons across different sublevels and orbitals gives rise to an element's electron configuration, which helps predict its chemical behavior. Each sublevel can hold a certain maximum number of electrons, influencing how atoms bond and interact with each other.