Step 1: Understand the question.
Radioactive materials give out three main rays: alpha, beta and gamma. We need the one that is made of high-energy photons and has no mass and no charge.
Step 2: Look at alpha radiation.
Alpha rays are helium nuclei. They have mass and a positive charge, so they do not fit.
Step 3: Look at beta radiation.
Beta rays are fast-moving electrons (or positrons). They have a small mass and carry charge, so they do not fit either.
Step 4: Look at neutron radiation.
Neutrons have no charge, but they do have mass. So they are also ruled out.
Step 5: Look at gamma radiation.
Gamma rays are electromagnetic waves made of photons. They have no mass and no charge, and they carry very high energy. They also travel at the speed of light and pass through matter easily.
Step 6: Conclude.
Only gamma radiation matches all the clues - high-energy photons with no mass and no charge.
\[ \boxed{\text{Gamma radiation}} \]