| +2 | +3 | +4 | |
|---|---|---|---|
| Eu | \(4f^7\) | \(4f^6\) | |
| Tm | \(4f^{13}\) | \(4f^{12}\) | |
| Sm | \(4f^6\) | \(4f^5\) | |
| Tb | \(4f^9\) | \(4f^8\) | \(4f^7\) |
| Yb | \(4f^{14}\) | \(4f^{13}\) | |
| Dy | \(4f^{10}\) | \(4f^9\) |
Hence, the pair \(Tb^{+4} Yb^{+2}\) have half filled and completely filled \(f\) subshells respectively.
The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V_z = 5\) V and the desired current in load is 5 mA. The unregulated voltage source can supply up to 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor \(R_s\) (shown in circuit) should be_______ \(\Omega\).
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is : 
\[ \left( \frac{1}{{}^{15}C_0} + \frac{1}{{}^{15}C_1} \right) \left( \frac{1}{{}^{15}C_1} + \frac{1}{{}^{15}C_2} \right) \cdots \left( \frac{1}{{}^{15}C_{12}} + \frac{1}{{}^{15}C_{13}} \right) = \frac{\alpha^{13}}{{}^{14}C_0 \, {}^{14}C_1 \cdots {}^{14}C_{12}} \]
Then \[ 30\alpha = \underline{\hspace{1cm}} \]

Lanthanoids are at the top of these two-row, while actinoids are at the bottom row.
Lanthanoids are inclusive of 14 elements, with atomic numbers 58-71:
These elements are also called rare earth elements. They are found naturally on the earth, and they're all radioactively stable except promethium, which is radioactive. A trend is one of the interesting properties of the lanthanoid elements, called lanthanide contraction.