**Explanation:**

A thermocouple is a device that measures temperature by utilizing the Seebeck effect. It consists of two different metals joined together at one end, known as the hot junction, and the other end is kept at a constant reference temperature, known as the cold junction. When there is a temperature gradient between the two junctions, it generates a voltage proportional to the temperature difference.

The relation between the neutral temperature (Tn) and the temperature of inversion (Ti) is given by the Thomson effect. The Thomson effect states that when a current flows through a homogeneous conductor, heat is absorbed or evolved at the rate of one watt per ampere per degree Celsius change in temperature.

To derive the relation between Tn and Ti, let's consider the following:

1. **Neutral Temperature (Tn):** It is the temperature at which the Seebeck coefficient of the two metals in the thermocouple becomes zero. At this temperature, the thermocouple produces no electromotive force (EMF) when there is no temperature difference between the junctions.

2. **Temperature of Inversion (Ti):** It is the temperature at which the polarity of the EMF produced by the thermocouple changes. Below Ti, the positive terminal of the thermocouple is at the hot junction, and above Ti, the positive terminal is at the cold junction.

Now, let's analyze the given scenario:

- The cold junction is kept at 0°C, which means its temperature is constant.
- The hot junction is kept at ToC, which can vary.
- Since the cold junction temperature is constant, any change in the EMF will be solely due to the temperature difference at the hot junction.

Based on the properties of a thermocouple, we can conclude that:

- The EMF produced by the thermocouple is directly proportional to the temperature difference between the hot and cold junctions.
- The EMF is zero at the neutral temperature (Tn).

To find the relation between Tn and Ti, we need to consider the behavior of the thermocouple when the hot junction's temperature is below or above Ti.

- When the hot junction's temperature is below Ti, the EMF is positive.
- When the hot junction's temperature is above Ti, the EMF is negative.

Therefore, we can conclude that the neutral temperature (Tn) is the average of the temperature of inversion (Ti) and the cold junction temperature.

Mathematically, it can be represented as:

Tn = (Ti + 0)/2

Simplifying the equation, we get:

Tn = Ti/2

Hence, the correct answer is option D: Tn = Ti/2.