Why sun produces continuous spectrum even through it is made up of mostly hydrogen gas?

Answer 1

The emission spectrum of hydrogen is not the primary contributor to the Sun's light. The Sun's outer layer is hot, and approximates a Black Body, which is a perfect emitter/absorber of light. A black body gives off a continuous spectrum of light whose peak wavelength is a function of Temperature alone, and not what the body is "made of". Imagine the Sun's surface as a roiling cauldron of fast moving charged particles, colliding with each other. Whenever a charged particle changes direction from a collision, it undergoes acceleration. Accelerated charges give off photons (synchrotron radiation). And, the frequency of that light as seen from a distance also undergoes a doppler shift based on the velocity of the emitter relative to us. All this is built into the effect of temperature. Our Sun is yellow; cooler stars are red, and hotter stars are blue. Divergences in calculating the Black Body Spectrum using classical physics were a major factor in the development of Quantum mechanics.