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Chapter 7: Problem 94

For each of the following elements, which set of orbitals is last to fill in the ground state? a. radium b. iodine c. gold d. uranium

Short Answer

Expert verified
In the ground state, the last set of orbitals to fill for each element is: a. Radium: \(7s\) b. Iodine: \(5p\) c. Gold: \(6s\) d. Uranium: \(5f\)

Step by step solution

01

Find the atomic number

For each element, we will find the atomic number, which is equal to the number of protons and electrons in a neutral atom. We can find atomic numbers on the periodic table: a. Radium (Ra): Atomic number = 88 b. Iodine (I): Atomic number = 53 c. Gold (Au): Atomic number = 79 d. Uranium (U): Atomic number = 92
02

Write the electron configuration

Using the Aufbau Principle, we will build the electron configuration for each element. The Aufbau Principle states that electrons are added to the lowest energy orbitals first before filling the higher energy ones. a. Radium (Ra): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2\) b. Iodine (I): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^5\) c. Gold (Au): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1 4f^{14} 5d^{10}\) d. Uranium (U): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^{3}\)
03

Identify the last set of orbitals to fill

Finally, we will find the last set of orbitals in the electron configuration for each element as this will be the orbitals that fill up last in the ground state. a. Radium (Ra): \(\underline{7s^2}\) b. Iodine (I): \(\underline{5p^5}\) c. Gold (Au): \(\underline{6s^1}\) d. Uranium (U): \(\underline{5f^{3}}\) In the ground state, the last set of orbitals to fill for each element is: a. Radium: \(7s\) b. Iodine: \(5p\) c. Gold: \(6s\) d. Uranium: \(5f\)

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Most popular questions from this chapter

Write equations corresponding to the following. a. the fourth ionization energy of Se b. the electron affinity of \(\mathrm{S}^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of Mg

In the ground state of element 115, Uup, a. how many electrons have \(n=5\) as one of their quantum numbers? b. how many electrons have \(\ell=3\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=1\) as one of their quantum numbers? d. how many electrons have \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

For hydrogen atoms, the wave function for the state \(n=3\) \(\ell=0, m_{\ell}=0\) is $$\psi_{300}=\frac{1}{81 \sqrt{3 \pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left(27-18 \sigma+2 \sigma^{2}\right) e^{-\sigma \beta}$$ where \(\sigma=r / a_{0}\) and \(a_{0}\) is the Bohr radius $\left(5.29 \times 10^{-11} \mathrm{m}\right) .$ Calculate the position of the nodes for this wave function.

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Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.
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