To calculate the Effective Atomic Number (EAN), use the following equation: \[ EAN = \text{Atomic number of the metal} - \text{Oxidation state} + 2 \times \text{Coordination number} \] Considering the complex \( [Co(NH_3)_6]^{3+} \):
- The atomic number of cobalt is 27.
- The oxidation state of cobalt in the complex is +3.
- The coordination number, representing the number of ligands bound to cobalt, is 6.
Applying these values to the formula: \[ EAN = 27 - 3 + 2 \times 6 = 36 \]
Explain the construction of a spherical wavefront by using Huygens' principle.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.