NaOH is prepared by the method

The correct option is D Castner-Kellner cell
NaOH is prepared by the method of castner kellner cell.
Hence, option D is the correct answer.

Chlorine should not come in contact with NaOH during electrolysis of NaCl, otherwise following reaction takes place.

$2NaOH+C{l}_2\to NaCl+NaOCl+H_{2}O$

To overcome this problem, the anode is separated from the cathode in the electrolytic cell by using a mercury cathode. The mercury cathode cell is known as caster-kellner cell.

The process of preparing NaOH solution by electrolysis of sodium chloride in castner- Kelner cell is called castner - Kellner process.

$\Rightarrow 2C{l}^{-}\to C{l}_2+2e^{-}\text{[Anode]}2N\stackrel{+}{a}+2e^{-}\to 2Na\text{[Cathode]}2Na+Hg\to Na-Hg\text{[Amalgam]}2Na-Hg+2H_{2}O\to 2NaOH+2Hg+H_2$

Theory
The Mercury Cathode cell (Castner-Kellner cell)
In this cell, mercury flows along the bottom of the cell and acts as a cathode.
The brine solution flows in the same direction and the anode consists of several graphite blocks.

Process of NaOH production in mercury cathode cell.

1. Brine is electrolyzed
2. Hydrogen has a high overvoltage at mercury cathode so sodium is preferentially discharged
3. Amalgam is formed with mercury
4. The Sodium amalgam reacts with water.
$2NaHg+2H_{2}O⟶2NaOH+2Hg+H_2$

Mercury is re-circulated to the cell, $H_2$ and $C{l}_2$ are the two essential by-products.

Preparation of pure NaOH
1. Commercial NaOH is purified with the help of alcohol.
2. NaOH dissolves in alcohol, while impurities remain insoluble.
3. The alcoholic filtrate is distilled. The alcohol distills off while pure solid sodium hydroxide is left behind