The way that quasars work is that you have an enormous black hole, typically at the center of a galaxy, that matter (stars, nebulae, etc.) is falling into. Because angular momentum is conserved and because everything in a galaxy will have some angular momentum, this matter collides with other matter as it falls in, and congregates into a spinning, whirlpool-like disk called an accretion disk. Accretion disks are known to happen on smaller scales, too; stars as they are born form from accretion disks, as do planets.

Because anything falling into a gravitational potential well will gain kinetic energy as it loses potential energy, colliding anything moving with such great kinetic energy will produce heat, heating up the accretion disk and causing it to radiate light. This radiated light is what we see from a quasar: the hot plasma as it spirals into the black hole.

Quasars do not produce specific wavelengths of light; they are more like stars that shine because of their heat, just a whole lot brighter than stars. The process is known as blackbody radiation: any object with a temperature will emit light at all frequencies, but the hotter it is, the more light it will emit, and the higher the peak frequency of the light that it does emit.

This is not a quantum effect, so it's difficult to count the photons, since blackbody radiation behaves more like waves than particles. As a consequence, it's difficult to answer exactly how many photons are being emitted.

An active quasar will emit light equal to the stars of a thousand (10³) galaxies. A typical galaxy shines about a hundred billion (10¹¹) times as brightly as the sun. The light emitted from the sun that reaches the Earth has a power-per-unit-area of 1.36 kilowatts per square meter. The distance from the sun to the Earth is 1.5 x 10¹¹ meters. You can use this distance to calculate a sphere of the radius of the Earth's orbit, and multiply that area by 1.36 kilowatts to get the total power output of the sun. Using the other numbers I gave you, you can then calculate how bright a quasar would be, measured in kilowatts.

The energy of a photon is given by the formula E = hf, where h is Plank's constant (6.626 x 10^-34 J s), and f is the frequency in hertz. The speed of light is 3 x 10⁸ meters per second. Most of the light coming out of a quasar is in the x-ray part of the spectrum. A medium-power x-ray photon might have a wavelength of 10^-10 meters. You can use this wavelength and the speed of light to calculate the frequency of such an x-ray, and then use E = hf to get the energy of that photon in joules. Once you have that energy, divide that into the power of a quasar shining as bright of a thousand galaxies and you will have an estimate of the number of photons that quasar emits each second. You do the algebra.