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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 predicted condensed electron configuration for element 126 is \[ \text{Rn} \ 7s^2 \ 5f^14 \ 6d^10 \ 7p^14. \]

Step by step solution

01

Identify the Previous Noble Gas

Before we can start building the electron configuration, we need to determine which noble gas element comes before element 126 in the periodic table. This will be the starting point for our electron configuration. The last noble gas with a lower atomic number than 126 is Radon (Rn), which has atomic number 86. So our starting point will be Rn.
02

Build the Electron Configuration

Starting with Rn as our base, we will add electrons one at a time, following the Aufbau principle. This principle states that electrons are added to orbitals of lower energy first, then orbitals of higher energy.
03

Step 2.1: Add Electrons to the 7s Orbital

After Rn, the next lowest energy orbital is the 7s orbital. A maximum of two electrons can occupy an s orbital. Thus, we add two electrons to the 7s orbital: Rn 7s^2
04

Step 2.2: Add Electrons to the 5f Orbital

The 5f orbital has a capacity for 14 electrons. After filling the 7s orbital, we add 14 electrons to the 5f orbital: Rn 7s^2 5f^14
05

Step 2.3: Add Electrons to the 6d Orbital

Moving on to the 6d orbital, it has a capacity for 10 electrons. We add 10 electrons to the 6d orbital: Rn 7s^2 5f^14 6d^10
06

Step 2.4: Add Electrons to the 7p Orbital

Finally, we reach the 7p orbital. Up to this point, we have already assigned (86 + 2 + 14 + 10) = 112 electrons. Since element 126 has 126 electrons, we need to add 14 more electrons to complete its electron configuration: Rn 7s^2 5f^14 6d^10 7p^14 In conclusion, the predicted condensed electron configuration for element 126 is \[ \text{Rn} \ 7s^2 \ 5f^14 \ 6d^10 \ 7p^14. \]

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Most popular questions from this chapter

Label each of the following statements as true or false. For those that are false, correct the statement. (a) Visible light is a form of electromagnetic radiation. (b) Ultraviolet light has longer wavelengths than visible light. (c) \(X\) rays travel faster than microwaves. (d) Electromagnetic radiation and sound waves travel at the same speed.

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

The series of emission lines of the hydrogen atom for which \(n_{1}=3\) is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed. (b) Calculate the wavelengths of the first three lines in the Paschen series - those for which \(n_{1}=4,5,\) and \(6 .\)

(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is \(2.94 \times 10^{14} \mathrm{s}^{-1} .\) (b) Calculate the energy of a photon of radiation whose wavelength is 413 nm. (c) What wavelength of radiation has photons of energy \(6.06 \times 10^{-19} \mathrm{J} ?\)

The following do not represent valid ground-state electron configurations for an atom either because they violate the Pauli exclusion principle or because orbitals are not filled in order of increasing energy. Indicate which of these two principles is violated in each example. (a) 1\(s^{2} 2 s^{2} 3 s^{1}\) (b) \([\mathrm{Xe}] 6 s^{2} 5 d^{4}(\mathbf{c})[\mathrm{Ne}] 3 s^{2} 3 d^{5} .\)
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