To determine the electron configurations of dysprosium (Dy) and americium (Am) using noble-gas notation, we need to follow these steps.
### Dysprosium (Dy)
1. Identify the number of electrons: Dysprosium (Dy) has an atomic number of 66, which means it has 66 electrons.
2. Determine the previous noble gas: The noble gas before dysprosium is xenon (Xe), which accounts for the first 54 electrons.
3. Write the remaining electron configuration: After accounting for xenon, we need to place the remaining 12 electrons (66 - 54 = 12). The electron configuration follows the order of filling subshells:
- Then add 2 electrons to the 6s subshell: 6s^2
- Next, add the remaining 10 electrons to the 4f subshell: 4f^10
Therefore, the noble-gas notation for dysprosium is:
[tex]\[ \boxed{[Xe] \, 6s^2 \, 4f^{10}} \][/tex]
### Americium (Am)
1. Identify the number of electrons: Americium (Am) has an atomic number of 95, which means it has 95 electrons.
2. Determine the previous noble gas: The noble gas before americium is radon (Rn), which accounts for the first 86 electrons.
3. Write the remaining electron configuration: After accounting for radon, we need to place the remaining 9 electrons (95 - 86 = 9). The electron configuration follows the order of filling subshells:
- Add 2 electrons to the 7s subshell: 7s^2
- Next, add the remaining 7 electrons to the 5f subshell: 5f^7
Therefore, the noble-gas notation for americium is:
[tex]\[ \boxed{[Rn] \, 7s^2 \, 5f^7} \][/tex]
In conclusion, the noble-gas notations for the electron configurations of dysprosium (Dy) and americium (Am) are:
For dysprosium (Dy):
[tex]\[ \boxed{[Xe] \, 6s^2 \, 4f^{10}} \][/tex]
For americium (Am):
[tex]\[ \boxed{[Rn] \, 7s^2 \, 5f^7} \][/tex]
