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Chapter 7: Problem 21

Which is higher in energy: the 2s or 2p orbital in hydrogen? Is this also true for helium? Explain

Short Answer

Expert verified
In hydrogen, there is no difference in energy between the 2s and 2p orbitals, as their energy levels depend only on the principal quantum number (n). However, for helium, a multi-electron atom, the 2p orbital has higher energy compared to the 2s orbital due to the influence of both the principal (n) and azimuthal (l) quantum numbers.

Step by step solution

01

Understand atomic orbitals and their energy levels

Atomic orbitals represent the regions in space where electrons are most likely to be found. These orbitals have different shapes and orientations and are classified into different types such as s, p, d, and f orbitals. The energy levels of these orbitals are determined by the principal quantum number (n) and the azimuthal quantum number (l). For the hydrogen atom, the energy of an orbital is determined only by the principal quantum number (n). However, for multi-electron atoms like helium, the energy of an orbital is influenced by both principal quantum number (n) and azimuthal quantum number (l). In general, when comparing orbitals with the same n value, those with a higher l value will have higher energy.
02

Identify electron configurations for hydrogen and helium

Electron configurations can be determined by the periodic table. For hydrogen, its electron configuration is 1s1, meaning it has only one electron in the 1s orbital. For helium, its electron configuration is 1s2, which indicates that it has two electrons in the 1s orbital.
03

Compare the energy levels of 2s and 2p orbitals in hydrogen

As mentioned earlier, for hydrogen, the energy level of an orbital is determined only by the principal quantum number (n). In this case, both 2s and 2p orbitals have the same n value of 2, so their energies are equal. Therefore, there is no difference in energy between the 2s and 2p orbitals for hydrogen.
04

Compare the energy levels of 2s and 2p orbitals in helium

For helium, a multi-electron atom, the energy of an orbital is influenced by both principal quantum number (n) and azimuthal quantum number (l). Since the 2s orbital has an l value of 0, while the 2p orbital has an l value of 1, the 2p orbital will have higher energy compared to the 2s orbital in helium.
05

Explain the comparison

In summary, for hydrogen, there is no difference in energy between the 2s and 2p orbitals, as their energy levels depend only on the principal quantum number (n). However, for helium, the 2p orbital has higher energy due to the influence of both principal (n) and azimuthal (l) quantum numbers.

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Most popular questions from this chapter

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?

Predict some of the properties of element 117 (the symbol is Uus, following conventions proposed by the International Union of Pure and Applied Chemistry, or IUPAC). a. What will be its electron configuration? b. What element will it most resemble chemically? c. What will be the formula of the neutral binary compounds it forms with sodium, magnesium, carbon, and oxygen? d. What oxyanions would you expect Uus to form?

One type of electromagnetic radiation has a frequency of 107.1 \(\mathrm{MHz}\) , another type has a wavelength of \(2.12 \times 10^{-10} \mathrm{m},\) and another type of electromagnetic radiation has photons with energy equal to \(3.97 \times 10^{-19} \mathrm{J} / \mathrm{photon}\) . Identify each type of electromagnetic radiation and place them in order of increasing photon energy and increasing frequency.

Small daily doses of lithium carbonate taken orally are often given to treat manic-depressive psychoses. This dosage maintains the level of lithium ion in the blood at about \(1 \times 10^{-3} \mathrm{mol} / \mathrm{L}\) . a. What is the formula of lithium carbonate? b. What mass of lithium ion is present per liter of blood in these patients?

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)
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