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Beryllium and Magnesium are small sized as compared to alkaline earth metals. (electrons stay more closer than in alkali earth metals). The alkali metals give out flame colour when the electrons shows change when it is being heated and after returning to their original state they have the same property that had earlier like their specific wavelength but this phenomena does not occur in Beryllium & Magnesium hence they do not impart colour to the flame.
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