Why smaller wavelengths have higher penetrating power? I've read that x-rays and gamma rays penetrate deeper whereas greater wavelengths like infrared don't go deep. Moreover, out of the two of radiations (alpha, beta) beta travels more in air on account of their small size. How and why does size/wavelength affects penetrating power?
 A: Matter is composed of atoms/molecules in the form of lattices, i.e. the atoms/molecules are organized a distance apart maintained by repulsive and attractive forces mainly electromagnetic ones.
As photons impinge on the solid they will interact with the electromagnetic interaction with the spill over field in the spaces between atoms, or directly hit atoms. The higher the  frequency of the wave the higher the energy of the photons $=hν$. For high energy photons,i.e. higher frequency light, the interstitial fields are in analogy as spiders webs to a fast projectile, i.e. the probability of interacting strongly is very small. Only if the photon hits an atom/molecule it will be deflected, and that has small probability (if one looks at the dimensions of lattices,) so it can travel deeper. In contrast infrared photons have a high probability to be absorbed in the binding energy levels of the solid, raising its temperature.
Alpha rays are really helium nuclei, have charge +2 and if their energy is low can be easily attracted and trapped  by the fringe fields, their energy turning into heat.  For high energy they can penetrate further, it all depends on the probabilities of scattering
Beta rays are really electrons coming from a decaying neutron , the electron has half the charge of the alpha particle so it will go further , with the same energy,   before interacting electromagnetically with any atoms/molecules in the air. Again one has to do specific calculations for specific energies.
