EM Spectrum
https://imagine.gsfc.nasa.gov/Images/science/EM_spectrum_compare_level1_lg.jpg

Gamma Radiation and X-Rays

Gamma rays and x-rays have some of the shortest wavelengths (and highest photon energies) in the EM spectrum: Gamma ranging from 10-10{10}^{-10} to 10-14{10}^{-14} meters and X-ray ranging from 10-9{10}^{-9} to 10-11{10}^{-11} meters. Judging from those wavelengths it is easy to notice that they also overlap in the EM spectrum. Unfortunately, there hasn't been a consensus on one single way to distinguish the two. (In some fields of physics the two are distinguished from their source of emission: Gamma rays are created by nuclear decay (which happens inside the nucleus) and x-rays are from the electrons outside the nucleus. While in astrophysics they are classified by their amount of photon energies: Gamma > 100keV (kilo electron-volts)> X-ray)


X-Rays:
Electromagnetic radiation with wavelengths ranging from 10-9{10}^{-9} to 10-11{10}^{-11} meters. X-ray photons are emitted when the incident electrons knock an inner orbital electron out of an atom.  Because of the penetrating ability, they are able to pass through many forms of matter, so most often they are medically and industrially used to examine internal structures.

X-ray Chest
http://e-waves.weebly.com/uploads/5/3/9/5/53955531/5015445.jpg?314

Hard x-rays (x-rays with high energy) are capable of going through relatively thick material without much of it being absorbed or scattered. So, that is why they are commonly used to create an image of the inside of visually opaque objects (like the x-ray image above).
But they also carry enough energy to ionize atoms and disrupt molecular bonds, which can make them harmful to living tissue. High doses of radiation exposure over a short period of time could cause radiation sickness, and low doses can potentially increase risk of radiation-induced cancer.

 
Gamma radiation:

Electromagnetic radiation with some of the shortest wavelength of the EM spectrum, ranging from 10-10{10}^{-10} to 10-14{10}^{-14} meters. They can have up to approximately 8 MeV (mega electron-volts) of photon energy. Gamma rays are emitted by an excited atomic nuclei during the process of passing to a lower excitation state (decay).

Gamma
                            Decay
https://upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Gamma_Decay.svg/1200px-Gamma_Decay.svg.png

Decay is defined to be "the spontaneous transformation of one radioactive nuclide into a daughter nuclide, which may be radioactive or may not, with the emission of one or more particles or photons". In short, it is when a nucleus of an atom loses a particle or photon.
Gamma rays are produced from gamma decay, which is form a decay that occurs from a nucleus that already has gone through alpha and beta decay, or in other words emitted alpha and beta particles. Since the nucleus had gone through two other forms of decay, meaning that it is left in an excited state, the process of entering an even lower energy state by emitting a gamma ray photon is gamma decay.

 
Since gamma rays have shorter wavelengths and thus higher energy than x-rays, they also have strong penetration power.

Penetration power all
https://www.nrc.gov/images/about-nrc/radiation/penetrating-power-rad.gif

Because they have similar ionizing qualities as x-rays, they also share similar risk factors.

 

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