A general knowledge but har question?

Question

The wavelengths of X-rays are much shorter than those of ultraviolet or visible light. Show QUANTITATIVELY why continued exposure to X-rays is more damaging than exposure to sunlight.

Answer 1

One way to do this might be-- consider the ionization energy of hydrogen-- it takes 13.6 eV to liberate an electron from a free hydrogen atom. If you have a photon with more energy than that, you'll get free electrons, which can cause damage. If you have a photon with lots more energy than that, you'll get highly energetic electrons, which really can screw things up. So, the first factor is to figure out the energy of liberated electrons.

Next, consider the penetration depth of x-rays. While ultraviolet light has a small penetration depth, and visible has much lower, x-rays can punch through your body, so damage can be caused at any depth-- UV light tends to cause skin cancer, but X-rays can give you cancer wherever...

Answer 2

They are different types on ionizing radiation. X-rays and gamma rays will ionize almost any molecule or atom, however, far ultraviolet, near ultraviolet and visible light are ionizing only to some molecules.

Answer 3

That would require measurements in a laboratory setting, not an a priori proof using mathematics.