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The essential distinction between X – Rays and $ \;\gamma $ rays is that,
A) $ \;\gamma - rays\; $ have smaller wavelength than X-rays
B) $ \;\gamma - rays\; $ Emanate from nucleus while X-rays emanate from outer part of the atom
C) $ \;\gamma - rays\; $ have greater ionizing power than X-rays
D) $ \;\gamma - rays\; $ are more penetrating than X-rays

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Answer
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Hint
Recollect about the radioactive decay process when a nucleus is in an excited state. It will be a gamma particle and when electrons go from one energy state to another they emit certain wavelengths of rays known as X- Rays.

Complete step by step answer
The essential distinction between $ \;\gamma - rays\; $ and X-rays is that $ \;\gamma - rays\; $ emanate from the nucleus. This happens during the radioactive decay process. A nucleus in an excited state has some extra energy which may release energy via gamma emission.
Electrons transitioning into a lower atomic orbital may emit an x-ray. Electrons propagating through a material may be accelerated (slowed down) by the electric field of a nucleus and will emit an x-ray. X-rays directly by accelerating a beam of electrons into a high atomic number metal, typically tungsten. The electrons are accelerated either by potential difference in x-ray tubes.
Option (B) is correct.

Note
i) Machine produced x-rays consist of a spectrum of energies, whereas gammas from a particular radionuclide have discrete energies..
ii) The term X-ray is used for photons with energies of about 1 keV and up that usually, but not always, come from man-made machines. Similarly, X-rays come from one of several processes that usually, but not always, involve electrons.