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Chapter 6: Problem 103

Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.

Short Answer

Expert verified
The condensed electron configuration of hypothetical element 126 is: \[[Rn]\ 7s^{2} \ 5f^{14} \ 6d^{10} \ 7p^{6}\]

Step by step solution

01

Determine the number of electrons to be placed into orbitals

Since the element has an atomic number of 126, it possesses 126 electrons. To find the electron configuration, we have to fill up the orbitals according to the Aufbau principle, which follows the order of increasing energy levels.
02

Familiarize with the Aufbau principle and the order of filling orbitals

The Aufbau principle dictates that electrons fill orbitals in order of increasing energy levels. The order can be followed using the mnemonic rule: \[1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p\] It represents the order of orbitals being filled by electrons. We will fill the orbitals with 126 electrons following this order.
03

Fill orbitals with 126 electrons using the Aufbau principle

Distributing 126 electrons in accordance with the Aufbau principle: \[1s^{2} \ 2s^{2} \ 2p^{6} \ 3s^{2} \ 3p^{6} \ 4s^{2} \ 3d^{10} \ 4p^{6} \ 5s^{2} \ 4d^{10} \ 5p^{6} \ 6s^{2} \ 4f^{14} \ 5d^{10} \ 6p^{6} \ 7s^{2} \ 5f^{14} \ 6d^{10} \ 7p^{6}\] Now we have placed all of the 126 electrons in their respective orbitals following the order.
04

Write condensed electron configuration

To write the condensed electron configuration, we first look for the last completely filled noble gas before element 126, which is Radon (Rn) with an atomic number of 86. The condensed electron configuration starts with the noble gas symbol [Rn] and continues with the configuration after the configuration of the corresponding noble gas. So, we have: \[[Rn]\ 7s^{2} \ 5f^{14} \ 6d^{10} \ 7p^{6}\] The condensed electron configuration of hypothetical element 126 is: \[[Rn]\ 7s^{2} \ 5f^{14} \ 6d^{10} \ 7p^{6}\]

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Most popular questions from this chapter

Place the following transitions of the hydrogen atom in order from shortest to longest wavelength of the photon emitted: \(n=5\) to \(n=2, n=4\) to \(n=3, n=8\) to \(n=4,\) and \(n=4\) to \(n=2\).

Einstein's 1905 paper on the photoelectric effect was the first important application of Planck's quantum hypothesis. Describe Planck's original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

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) \(n=5, l=2\), \(m_{l}=0 .\)

(a) Using Equation 6.5 , calculate the energy of an electron in the hydrogen atom when \(n=3\) and when \(n=6\). Calculate the wavelength of the radiation released when an electron moves from \(n=6\) to \(n=3 .(\mathbf{b})\) Is this line in the visible region of the electromagnetic spectrum?

Consider a transition in which the electron of a hydrogen atom is excited from \(n=1\) to \(n=\infty\). (a) What is the end result of this transition? (b) What is the wavelength of light that must be absorbed to accomplish this process? (c) What will occur if light with a shorter wavelength than that in part (b) is used to excite the hydrogen atom? (d) How are the results of parts \((\mathrm{b})\) and \((\mathrm{c})\) related to the plot shown in Exercise \(6.88 ?\)
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