Conversion of Ethanol to Ethyl Bromide (A): Ethanol reacts with bromine in the presence of red phosphorus to form ethyl bromide. \[ CH_3CH_2OH + Br_2 \xrightarrow{\text{red P}} CH_3CH_2Br + HBr \] So, \( A = \) Ethyl Bromide \( (CH_3CH_2Br) \).
Conversion of Ethyl Bromide to Propanenitrile (B): Ethyl bromide reacts with alcoholic potassium cyanide \( (KCN) \) to form propanenitrile. \[ CH_3CH_2Br + KCN \rightarrow CH_3CH_2CN + KBr \] So, \( B = \) Propanenitrile \( (CH_3CH_2CN) \).
Conversion of Propanenitrile to Propylamine (C): Propanenitrile undergoes reduction with lithium aluminum hydride \( (LiAlH_4) \) in ether to form propylamine. \[ CH_3CH_2CN + 4[H] \xrightarrow{\text{LiAlH}_4, \text{Ether}} CH_3CH_2CH_2NH_2 \] So, \( C = \) Propylamine \( (CH_3CH_2CH_2NH_2) \).
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 ___________.