The Sun’s surface puts out light at all wavelengths, but the surface isn’t solid. It’s a gas, and it tapers off with height. Normally, a thin gas in space emits light at very specific colors as electrons jump from one energy level to another in the individual atoms. But compressed gas in the thicker, denser part of the Sun mashes together all those energies, spreading them out, so it emits white light (that layer of the Sun is called the photosphere). Above that layer, where the gas is thinner (in a layer called the chromosphere), the hydrogen does emit light at specific colors. One of these, Hα, is in the red part of the spectrum, and in fact hot, thin hydrogen emits very strongly in Hα.