To determine the electronic configurations of tetravalent terbium (Tb) and divalent ytterbium (Yb), we will follow these steps:
### Step 1: Identify the Atomic Numbers
- The atomic number of Terbium (Tb) is 65.
- The atomic number of Ytterbium (Yb) is 70.
### Step 2: Write the Electronic Configuration for Terbium (Tb)
- The electronic configuration of an element can be derived from the previous noble gas configuration. For Tb, we start with Xenon (Xe), which has an atomic number of 54.
- The remaining electrons after Xenon for Tb are:
\( 65 - 54 = 11 \) electrons.
- The configuration can be written as:
\[
\text{Xe} \, 6s^2 \, 4f^{9}
\]
(This accounts for the 2 electrons in the 6s subshell and 9 electrons in the 4f subshell).
### Step 3: Determine the Configuration for Tetravalent Terbium (Tb^4+)
- Tetravalent means that Tb has lost 4 electrons. The electrons are removed first from the 6s and then from the 4f subshell.
- Removing 2 electrons from the 6s subshell and 2 electrons from the 4f subshell gives:
\[
\text{Xe} \, 6s^0 \, 4f^{7}
\]
- Therefore, the electronic configuration for tetravalent terbium (Tb^4+) is:
\[
\text{Xe} \, 4f^{7}
\]
### Step 4: Write the Electronic Configuration for Ytterbium (Yb)
- For Yb, starting from Xenon (Xe) again, we have:
\( 70 - 54 = 16 \) electrons remaining.
- The configuration can be written as:
\[
\text{Xe} \, 6s^2 \, 4f^{14}
\]
(This accounts for the 2 electrons in the 6s subshell and 14 electrons in the 4f subshell).
### Step 5: Determine the Configuration for Divalent Ytterbium (Yb^2+)
- Divalent means that Yb has lost 2 electrons. These electrons are removed from the 6s subshell first:
\[
\text{Xe} \, 6s^0 \, 4f^{14}
\]
- Therefore, the electronic configuration for divalent ytterbium (Yb^2+) is:
\[
\text{Xe} \, 4f^{14}
\]
### Final Answer
- The electronic configuration of tetravalent terbium (Tb^4+) is:
\[
\text{Xe} \, 4f^{7}
\]
- The electronic configuration of divalent ytterbium (Yb^2+) is:
\[
\text{Xe} \, 4f^{14}
\]
