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. d. 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 D are false.

Step-by-step solution

Statement A

The statement suggests that the \(2s\) orbital in a hydrogen atom is larger than the \(3s\) orbital. However, the size of an orbital increases with an increase in the principal quantum number (n). Since n value for \(3s\) orbital (n=3) is larger than that for \(2s\) orbital (n=2), the \(3s\) orbital is actually larger than the \(2s\) orbital. Therefore, the statement is false.

Statement B

The statement suggests that the Bohr model of the hydrogen atom is incorrect. Indeed, the Bohr model was a crucial early step in understanding atomic structure, but it has significant limitations and inaccuracies, particularly for multi-electron atoms. With the development of quantum mechanics, the shortcomings of the Bohr model were addressed and a more accurate model of the atom was developed. Therefore, the statement is true.

Statement C

The statement suggests that the hydrogen atom has quantized energy levels. This is a fundamental concept in quantum mechanics and atomic structure, where the electrons in an atom can only have specific, discrete energy levels. This principle has been experimentally verified and is essential for explaining atomic spectra. Therefore, the statement is true.

Statement D

The statement suggests that an orbital is the same as a Bohr orbit. However, Bohr orbits represent circular paths of electrons around the nucleus in the Bohr model, while orbitals represent the probability distribution of electron locations around the nucleus in the quantum mechanical model. Although both concepts are related to the electronic structure of atoms, they are not the same. Therefore, the statement is false.

Statement E

The statement suggests that the third energy level has three sublevels: \(s, p,\) and \(d\). In quantum mechanics, energy levels can contain sublevels determined by the azimuthal quantum number (l), which ranges from 0 to n-1. For the third energy level (n=3), the azimuthal quantum number (l) can be 0, 1, and 2. These values correspond to the \(s\), \(p\), and \(d\) sublevels, respectively. Therefore, the statement is true. In summary, statements B, C, and E are true, while statements A and D are false.

Key concepts

Bohr model

The Bohr model is an early theory of atomic structure featuring electrons in fixed circular orbits around a central nucleus. Although significant for its time, this model had key limitations. The most notable issue is its inability to accurately describe atoms with more than one electron. In Bohr's model, electrons travel in circular paths with quantized energies, meaning they occupy specific energy levels. However, this model didn't account for electron-electron interactions present in multi-electron atoms. Thus, while it provides a starting foundation for understanding atomic theory, it has been superseded by more comprehensive quantum mechanical models. These modern approaches view electron orbitals as probability clouds, offering a more accurate and nuanced depiction than Bohr's fixed orbits.

quantized energy levels

In atomic physics, quantized energy levels refer to the concept that electrons can only occupy specific, distinct energy states. Electrons within an atom do not possess a continuous spectrum of energies; instead, they can only have particular energy values. This principle is crucial in understanding atomic spectra, as electrons transition between energy levels by absorbing or emitting precise amounts of energy, often visible as light of specific colors. These transitions are known as quantum leaps, distinguishing electron behavior from classical predictions. Quantized energy levels mean each energy level has a unique position and energy requirement. Thus, understanding this concept is vital for grasping the behavior and interactions of electrons in atoms.

electron sublevels

Electron sublevels provide further division of energy levels within an atom and are shaped by the azimuthal quantum number. For an energy level denoted by the principal quantum number (n), sublevels range from 0 to -1. Each of these sublevels corresponds to specific electron clouds with distinct shapes and energies, known as orbitals:

• The first sublevel (l = 0) is called the 's' sublevel.
• The second sublevel (l = 1) is called the 'p' sublevel.
• The third sublevel (l = 2) is called the 'd' sublevel, and so on.

For example, the third energy level (n = 3) can contain three sublevels: 3s, 3p, and 3d. Each sublevel consists of one or more orbitals, where electrons are likely to be found. Understanding these sublevels and their corresponding orbitals is key to predicting and explaining chemical behavior and bonding.