People who carry their essential oils onto airplanes want to know if the x-rays at the security gates will damage them. The answer is probably yes, but only to a very minor extent and what damage occurs is repairable.
When a high frequency photon of electromagnetic energy (like an x-ray) makes a direct hit on a molecule, it can splinter it into pieces. Fragments of a molecule are free radicals, electrically unbalanced ions or groups of atoms looking for their missing parts.
Free radicals are not nice to have floating around in your body because they will grab electrons and atoms from your tissues, accelerating the aging process, damaging organs and tissues, and, in some cases, causing cellular mutations that eventually become cancer. That is why when we are personally exposed to high doses of x-rays, gamma rays, nuclear radiation, or other high frequency electromagnetic energies we can suffer various levels of radiation sickness.
Being irradiated by x-rays and other high frequency electromagnetic energy is not such a problem for essential oils as for people because oils contain no living cells that can be damaged and result in sickness. All that can happen in an oil is that a few molecules may be fractured into pieces. Percent wise It won't be many, say one in 10,000. That is because molecules and compounds are mostly space through which x-rays can pass harmlessly. It is only with a direct hit that a molecule is fractured.
Interestingly, one of the healing properties of essential oils is that they can remove free radicals from our bodies. This is because they are powerful antioxidants. Antioxidants are substances that can neutralize the damaging effects of free radicals and remove them from our bodies. Fresh fruits and vegetables are high in antioxidants, but no food is as high In antioxidants as most essential oils, which are many times more concentrated than undistilled produce. Table Thirty on the next page lists eighteen representative essential oils and an equal number of fruits and vegetables with their ORAC scores. ORAC (Oxygen Radical Absorbance Capacity) is a scale developed by the U.S. Department of Agriculture in cooperation with scientists at Tufts University, Boston, Massachusetts. The scale measures the antioxidant potential of various foods and substances.
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Reference: The above excerpt is paraphrased from Dr. Stewart's book, The Chemistry of Essential Oils Made Simple (God's Love Manifest in Molecules) 896 pages.