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Chapter 7: Problem 168

Which of the following statements is (are) true? a. The 2\(s\) orbital in the hydrogen atom is larger than the 3s 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
The short answer is: statements b, c, and e are true. Statement b is true because the Bohr model was found to be incorrect and has been replaced by the more accurate quantum mechanical model. Statement c is true since both the Bohr model and the quantum mechanical model agree that the energy levels of a hydrogen atom are quantized. Lastly, statement e is true as the third energy level (n=3) has three sublevels, which are s, p, and d orbitals.

Step by step solution

01

Understand electron configuration and orbitals in the hydrogen atom

The hydrogen atom has only one electron. In order to determine the size of an orbital, we need to understand the electron configuration and the shapes of various orbitals. The electron configuration of hydrogen is 1s¹. The s orbital has a spherical shape and is the lowest energy level. Different energy levels have different sizes and shapes of their s orbitals.
02

Comparing 2s and 3s orbitals in hydrogen atom

According to the modern quantum mechanical model of the atom, the size of an orbital increases with the increasing principal quantum number (n). Since the principal quantum number of the 3s orbital (n=3) is greater than the 2s orbital (n=2), the 3s orbital is larger than the 2s orbital. Therefore, statement a is false.
03

Evaluate the Bohr model of the hydrogen atom

The Bohr model was an early model of the hydrogen atom, which suggested that electrons travel around the nucleus in fixed circular orbits and that the energy of an electron was quantized. Although the Bohr model successfully explained the energy levels in the hydrogen atom, it could not accurately explain the behavior of electrons in more complicated atoms. Consequently, it has been replaced by the more accurate and general quantum mechanical model of the atom. Thus, statement b is true, although it was a significant step in understanding the hydrogen atom.
04

Determine if the hydrogen atom has quantized energy levels

Both the Bohr model and the quantum mechanical model agree that the energy levels of a hydrogen atom are quantized. This means that electrons in a hydrogen atom can only occupy specific energy levels. This fact has been confirmed through various experiments and observations, such as the hydrogen spectral lines. Therefore, statement c is true.
05

Compare an orbital to a Bohr orbit

An orbital, according to the quantum mechanical model, is a mathematical description of the probability of finding an electron within a specific region around the nucleus. On the other hand, a Bohr orbit represents a fixed circular path in which an electron travels around the nucleus. The concept of an orbital is a more accurate representation of the behavior of electrons in atoms. Thus, an orbital is not the same as a Bohr orbit. Therefore, statement d is false.
06

Identify the sublevels of the third energy level

In the quantum mechanical model, each energy level has a specific number of sublevels. The number of sublevels is equal to the principal quantum number (n). For the third energy level (n=3), there should be three sublevels, which are s, p, and d orbitals. So, statement e is true. In conclusion: a. False b. True c. True d. False e. True

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Most popular questions from this chapter

An ion having a \(4+\) charge and a mass of 49.9 u has 2 electrons with principal quantum number \(n=1,8\) electrons with \(n=2\) and 10 electrons with \(n=3 .\) Supply as many of the properties for the ion as possible from the information given. (Hint: In forming ions for this species, the 4\(s\) electrons are lost before the 3\(d\) electrons.) a. the atomic number b. total number of \(s\) electrons c. total number of \(p\) electrons d. total number of \(d\) electrons e. the number of neutrons in the nucleus f. the ground-state electron configuration of the neutral atom

The ionization energy for a 1\(s\) electron in a silver atom is $2.462 \times 10^{6} \mathrm{kJ} / \mathrm{mol} .$ a. Determine an approximate value for \(Z_{\text { eff }}\) for the \(A g 1 s\) electron. Assume the Bohr model applies to the 1 s electron. \(Z_{\mathrm{eff}}\) is the apparent nuclear charge experienced by the electrons. b. How does \(Z_{\text { eff }}\) from part a compare to \(Z\) for Ag? Rationalize the relative numbers.

Answer the following questions assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell,\) and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of 4\(f\) orbitals be able to hold?

Answer the following questions based on the given electron configurations, and identify the elements. a. Arrange these atoms in order of increasing size: $[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{6} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{1} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{3}$ b. Arrange these atoms in order of decreasing first ionization energy: [Ne $3 s^{2} 3 p^{5} ;[\operatorname{Ar}] 4 s^{2} 3 d^{10} 4 p^{3} ;[\operatorname{Ar}] 4 s^{2} 3 d^{10} 4 p^{5}$

One bit of evidence that the quantum mechanical model is “correct” lies in the magnetic properties of matter. Atoms with unpaired electrons are attracted by magnetic fields and thus are said to exhibit paramagnetism. The degree to which this effect is observed is directly related to the number of unpaired electrons present in the atom. Consider the ground-state electron configurations for Li, N, Ni, Te, Ba, and Hg. Which of these atoms would be expected to be paramagnetic, and how many unpaired electrons are present in each paramagnetic atom?
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