Lanthanide Contraction: The term "Lanthanide contraction" describes the progressive decrease in the atomic and ionic sizes of the elements in the lanthanide series. This phenomenon is attributed to the ineffective shielding of the nuclear charge by the 4f electrons.
Reaction of Acidified \( K_2Cr_2O_7 \) with \( H_2S \): \[ K_2Cr_2O_7 + 3H_2SO_4 + 3H_2S \rightarrow 2Cr_2(SO_4)_3 + 7H_2O + 3S \] This reaction illustrates the oxidizing power of potassium dichromate in an acidic medium, where it converts hydrogen sulfide to sulfur.
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 ___________.