To determine the noble-gas notation for lead (Pb), we should look at its position in the periodic table and use the nearest preceding noble gas as a reference. Lead (Pb) has an atomic number of 82. The nearest preceding noble gas is Xenon (Xe) with an atomic number of 54.
Lead belongs to period 6 and its electron configuration can be built starting from the noble-gas core of Xenon ([tex]\( [Xe] \)[/tex]). After Xenon, we continue to fill the electron orbitals in the following sequence based on the Aufbau principle (which dictates the order in which electron orbitals are filled):
1. 6s orbital
2. 4f orbital
3. 5d orbital
4. 6p orbital
Now let's write down the electron configuration step-by-step:
1. Starting with Xenon (Xe) -- which accounts for the first 54 electrons:
[tex]\[ [Xe] \][/tex]
2. Next, fill the 6s orbital (which can hold 2 electrons):
[tex]\[ 6s^2 \][/tex]
3. Then, fill the 4f orbital (which can hold 14 electrons):
[tex]\[ 4f^{14} \][/tex]
4. Next, fill the 5d orbital (which can hold 10 electrons):
[tex]\[ 5d^{10} \][/tex]
5. Finally, fill the 6p orbital (which can hold 6 electrons but for lead only 2 are needed):
[tex]\[ 6p^2 \][/tex]
Putting it all together, the noble-gas notation for the electron configuration of lead ([tex]\( Pb \)[/tex]) is:
[tex]\[ [Xe] 6s^2 4f^{14} 5d^{10} 6p^2 \][/tex]
Thus, the correct answer is:
[tex]\[ [Xe] 6s^2 4f^{14} 5d^{10} 6p^2 \][/tex]
