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Chapter 7: Problem 158

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

Expert verified
Statements B, C, and E are true, while statements A and D are false.

Step by step solution

01

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.
02

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.
03

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.
04

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.
05

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.

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