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Chapter 6: Problem 67

(a) For an He+ ion, do the \(2 s\) and \(2 p\) orbitals have the same energy? If not, which orbital has a lower energy? (b) If we add one electron to form the He atom, would your answer to part (a) change?

Short Answer

Expert verified
(a) In an He+ ion, the 2s and 2p orbitals have the same energy, as there is no electron shielding effect involved. (b) When an electron is added to form a neutral He atom, the 2s orbital will have lower energy than the 2p orbital due to electron shielding effects.

Step by step solution

01

Analyze the He+ ion

In an He+ ion, there is only one electron present. As a result, there will be no electron-electron interactions and no shielding effect, which often cause energy differences between different orbitals (such as 2s and 2p).
02

Compare the energy of 2s and 2p orbitals in He+ ion

Since there is no electron shielding effect in an He+ ion, the 2s and 2p orbitals will have the same energy. This is because they have the same principal quantum number (n=2), and the electron shielding effect is the primary factor that causes energy differences between orbitals with the same principal quantum number.
03

Analyze the He atom

When we add an electron to form a neutral helium atom (He), there are now 2 electrons present. The shielding effect will come into play, as electrons in different orbitals will experience different amounts of shielding from each other.
04

Compare the energy of 2s and 2p orbitals in He atom

In a neutral helium atom, the more the electron in an orbital is shielded, the less the net attractive force from the nucleus it experiences, and thus the higher the energy of the orbital. In general, s orbitals experience less effective shielding than p orbitals do. Therefore, in a neutral helium atom, the 2s orbital would have lower energy than the 2p orbital.
05

Final Answer (a)

In an He+ ion, the 2s and 2p orbitals have the same energy.
06

Final Answer (b)

When an electron is added to form a neutral He atom, the energies of the 2s and 2p orbitals change due to electron shielding effects. The 2s orbital will have lower energy than the 2p orbital in the neutral helium atom.

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Most popular questions from this chapter

What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) \(n=3, m_{l}=-1 ;\) (b) \(n=4, l=2\); (c) \(n=4, l=3, m_{l}=-2 ;\) (d) \(n=5, l=2\), \(m_{l}=0 .\)

For each element, indicate the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) sodium, (b) sulfur, (c) fluorine.

In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015 . The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers \((2.6\) billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

If human height were quantized in 1 -cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of \(6 \mathrm{~cm}\), or (iv) the child's height would increase in "jumps" of \(1 \mathrm{~cm}\) at a time?

(a) Account for formation of the following series of oxides in terms of the electron configurations of the elements and the discussion of ionic compounds in Section 2.7: $\mathrm{K}_{2} \mathrm{O}, \mathrm{CaO}, \mathrm{Sc}_{2} \mathrm{O}_{3}, \mathrm{TiO}_{2}, \mathrm{~V}_{2} \mathrm{O}_{5}, \mathrm{CrO}_{3} .(\mathbf{b})$ Name these oxides. (c) Consider the metal oxides whose enthalpies of formation (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) are listed here. Calculate the enthalpy changes in the following general reaction for each case: $$\mathrm{M}_{n} \mathrm{O}_{m}(s)+\mathrm{H}_{2}(g) \longrightarrow n \mathrm{M}(s)+m \mathrm{H}_{2} \mathrm{O}(g)$$ (You will need to write the balanced equation for each case and then compute \(\left.\Delta H^{\circ} .\right)\) (d) Based on the data given, estimate a value of \(\Delta H_{f}^{\circ}\) for \(\mathrm{Sc}_{2} \mathrm{O}_{3}(s)\)
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