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Chapter 7: Problem 70

List the hydrogen orbitals in increasing order of energy.

Short Answer

Expert verified
The energy levels of hydrogen orbitals increase in the following order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (and so on).

Step by step solution

01

Understanding Hydrogen Atom

A hydrogen atom has only one electron. In an atom, the electron configuration refers to the distribution of electrons in atomic or molecular orbitals. For the hydrogen atom, this task is straightforward as there is only one electron to place in an orbital.
02

Energy Levels in Hydrogen Atom

The energy levels of hydrogen are determined by the quantum numbers: n is the principal quantum number, and l is the azimuthal quantum number. The energy of an orbital increases as the sum of the quantum numbers, (n + l), increase. In a hydrogen atom, the 1s level (n=1, l=0) is the lowest energy level.
03

Listing the Orbitals by Increasing Energy Levels

Following the (n+l) rule, if two orbitals have the same (n+l) value, the one with lower n has lower energy. Therefore, the energy levels of hydrogen orbitals increase in the following order - 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (and so on).

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Most popular questions from this chapter

Briefly describe Bohr's theory of the hydrogen atom and how it explains the appearance of an emission spectrum. How does Bohr's theory differ from concepts of classical physics?

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in \(\mathrm{nm}\) ) of such a proton moving at \(2.90 \times\) \(10^{8} \mathrm{~m} / \mathrm{s}\). (Mass of a proton \(\left.=1.673 \times 10^{-27} \mathrm{~kg} .\right)\)

Considering only the ground-state electron configuration, are there more diamagnetic or paramagnetic elements? Explain.

The sun is surrounded by a white circle of gaseous material called the corona, which becomes visible during a total eclipse of the sun. The temperature of the corona is in the millions of degrees Celsius, which is high enough to break up molecules and remove some or all of the electrons from atoms. One way astronomers have been able to estimate the temperature of the corona is by studying the emission lines of ions of certain elements. For example, the emission spectrum of \(\mathrm{Fe}^{14+}\) ions has been recorded and analyzed. Knowing that it takes \(3.5 \times 10^{4} \mathrm{~kJ} / \mathrm{mol}\) to convert \(\mathrm{Fe}^{13+}\) to \(\mathrm{Fe}^{14+},\) estimate the temperature of the sun's corona.

An electron in the hydrogen atom makes a transition from an energy state of principal quantum numbers \(n_{\mathrm{i}}\) to the \(n=2\) state. If the photon emitted has a wavelength of \(434 \mathrm{nm}\), what is the value of \(n_{\mathrm{i}}\) ?
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