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Chapter 4: Problem 6

The value of the ionization energy of He given in Table 1 is described as being consistent with a model in which the two electrons in He are in a "shell" at approximately the same distance from the nucleus as the one electron in \(\mathrm{H}\). Use the Coulombic Potential Energy equation, \(V=\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{~d}}\) to explain how this conclusion can be reached. Hint: recall the relationship between \(V\) and \(\mathrm{IE}_{1}\).

Short Answer

Expert verified
The ionization energy of He is twice that of H because in He there are two electrons being removed, each contributing a potential energy equal to that of the single electron in H. This is consistent with the given model.

Step by step solution

01

Understanding of Key Terms

The first step is making sure all the key terms and equations are understood. The Coulombic Potential Energy (V) equation shows the relationship between two charged entities (q1 and q2), their separation distance (d), and a constant (k). Ionization Energy (IE) is the energy required to remove an electron from an atom.
02

Identifying the Variables

In order to apply the equation, we need to identify the variables. In the case of Helium (He), there are two electrons, so q1 and q2 will both correspond to the charge of an electron. The distance d will be the same as in the Hydrogen model, since according to the problem, both electrons in He are in a 'shell' that is at approximately the same distance from the nucleus as the one electron in H.
03

Linking Potential Energy and Ionization Energy

Since ionization is the process of removing an electron (which has negative charge) from an atom, the Ionization Energy is associated with the potential energy V. Thus, the ionization energy of Helium can be calculated as being twice the potential energy, since we are removing two negatively charged particles as compared to one in the case of Hydrogen.
04

Conclusion

With the understanding that the potential energy of He's two electrons is twice as large due to the two negatively charged electrons being removed, we can conclude that the ionization energy being twice that of Hydrogen fits the model description of two electrons being approximately the same distance from the nucleus as the one electron in Hydrogen.

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Most popular questions from this chapter

Using grammatically correct sentences: a) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{He}\) is greater than \(\mathrm{IE}_{1}\) for \(\mathrm{H}\). b) provide a possible explanation for why \(\mathrm{IE}_{1}\) for \(\mathrm{Li}\) is less than \(\mathrm{IE}_{1}\) for He.

For atoms with many electrons, not all electrons are at the same distance from the nucleus. In this case, which electron would have the lowest ionization energy: the electron that is closest to the nucleus or the electron that is farthest from the nucleus? Explain.

Based on what you have learned so far in this course, predict the relationship between \(\mathrm{IE}_{1}\) and atomic number by making a rough graph of \(\mathrm{IE}_{1}\) vs. atomic number. Discuss possible ideas with your team and decide which one you think makes the most sense. DO NOT PROCEED TO THE NEXT PAGE UNTIL YOU HAVE MADE YOUR PREDICTED GRAPH.

Recall that the IE of \(\mathrm{H}\) is \(1.31 \mathrm{MJ} / \mathrm{mole}\). If all three electrons in Li were in the first shell at a distance equal to that of hydrogen, which of the following values would be the better estimate of the IE \(_{1}\) of Li: \(3.6 \mathrm{MJ} / \mathrm{mole}\) or \(0.6 \mathrm{MJ} / \mathrm{mole}\) ? Explain your reasoning.

a) How much energy does it take to remove an electron from one \(\mathrm{H}\) atom? b) How much total energy would it take to remove the electrons from two H atoms? c) How much total energy would it take to remove the electrons from a mole of \(\mathrm{H}\) atoms? Express this energy in units of \(\mathrm{J}\) and in units of \(\mathrm{MJ} .\)
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