Convert the following:
(i) acetaldehyde to isopropyl alcohol.
(ii) cumene to phenol.
(iii) anisole to phenol. Write two uses of neon.
Acetaldehyde \( (CH_3CHO) \) can be converted to isopropyl alcohol \( (CH_3CH(OH)CH_3) \) through the following steps:
1. Aldol Condensation: \[ 2CH_3CHO \xrightarrow{\text{Dil. NaOH}} CH_3CH(OH)CH_2CHO \]
2. Catalytic Hydrogenation: \[ CH_3CH(OH)CH_2CHO + H_2 \xrightarrow{\text{Ni, Heat}} CH_3CH(OH)CH_3 \] Thus, acetaldehyde undergoes aldol condensation followed by hydrogenation to yield isopropyl alcohol.
Cumene \( (C_6H_5CH(CH_3)_2) \) is converted to phenol by the cumene hydroperoxide process:
1. Oxidation of Cumene: \[ C_6H_5CH(CH_3)_2 + O_2 \rightarrow C_6H_5C(CH_3)_2OOH \]
2. Acidic Hydrolysis: \[ C_6H_5C(CH_3)_2OOH \xrightarrow{H^+} C_6H_5OH + CH_3COCH_3 \] Thus, cumene is oxidized to cumene hydroperoxide, which undergoes acid hydrolysis to give phenol and acetone as a byproduct.
Anisole to Phenol. Write two uses of neon.
Anisole \( (C_6H_5OCH_3) \) can be converted to phenol \( (C_6H_5OH) \) via hydrolysis using hydrobromic acid: \[ C_6H_5OCH_3 + HBr \xrightarrow{\text{Heat}} C_6H_5OH + CH_3Br \]
Neon (Ne) is a noble gas with various applications. Two important uses include:
1. Illumination: Used in neon lights and advertising signs.
2. Cryogenics: Used in high-performance cooling systems, especially in refrigeration.
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 ___________.