The reaction responsible for the radiant energy of the Sun is

The correct option is nuclear fusion.

Detailed Explanation:
The Sun produces an immense amount of radiant energy (light and heat) through a process known as nuclear fusion. This process occurs deep within the Sun's core, where temperatures and pressures are extremely high.

During nuclear fusion, lighter atomic nuclei combine to form a heavier nucleus. In the case of the Sun, the primary reaction is the fusion of hydrogen nuclei (protons) into helium nuclei. The general representation of this fusion process can be written as:

$$4H_1^1\to {\mathrm{He}}_2^4+2e_{+1}^0+2\nu +\text{Energy}$$

In this reaction, the total mass of the resulting helium nucleus is slightly less than the sum of the masses of the individual hydrogen nuclei. This difference in mass, known as the mass defect, is converted directly into energy according to Einstein's mass-energy equivalence equation:

$$E=m{c}^2$$

Here, $E$ represents the energy produced, $m$ is the mass lost (mass defect), and $c$ is the speed of light. Because the speed of light is extremely large, even a tiny amount of mass conversion yields a colossal amount of energy.

Why other options are incorrect:
- Nuclear fission is the splitting of a heavy nucleus into lighter nuclei (as used in nuclear power plants on Earth), which is not the process powering the Sun.
- Chemical reactions and combustion involve the rearrangement of electrons between atoms. These chemical processes release far too little energy to sustain the Sun's output for billions of years.