Problem 98 - Chemistry: The Central Science

Question

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.

Step-by-Step Solution

Answer

The condensed electron configuration of element 126 is: [Rn] \(7s^2 5f^{14} 6d^{10} 7p^4\).

Step 1: Determine the number of electrons

Element 126 will have 126 protons and, since it is neutral, 126 electrons. We will be placing these 126 electrons in the respective atomic orbitals according to the rules of electron configuration.

Step 2: Recall the order of orbital filling

Following the Aufbau principle, we will place electrons in orbitals in this order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

Step 3: Fill the orbitals with electrons

We will fill the orbitals with electrons, keeping in mind that each orbital can hold a maximum of 2 electrons, each subshell (s, p, d, f) can hold 2, 6, 10, or 14 electrons, respectively: 1. 1s: 2 2. 2s: 2 3. 2p: 6 4. 3s: 2 5. 3p: 6 6. 4s: 2 7. 3d: 10 8. 4p: 6 9. 5s: 2 10. 4d: 10 11. 5p: 6 12. 6s: 2 13. 4f: 14 14. 5d: 10 15. 6p: 6 16. 7s: 2 17. 5f: 14 18. 6d: 10 19. 7p: 4 (We only have 4 electrons left to place)

Step 4: Write out the complete electron configuration

Writing out the electron configuration using the number of electrons assigned to each orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^{14} 6d^{10} 7p^4\)

Step 5: Condense the electron configuration

To express this in condensed electron configuration form, we find the nearest noble gas with a lower atomic number than element 126. In this case, it is the noble gas with the electron configuration that comes before 7p - Radon (Rn). Radon electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6\) Now we can replace the electron configuration of Radon (Rn) in our full electron configuration with [Rn]: \(\text{Element 126 condensed electron configuration:}\) [Rn] \(7s^2 5f^{14} 6d^{10} 7p^4\)