Beryllium and magnesium do not give colour to flame wherea

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On heating an alkali earth metal or its salt, the electrons are excited easily to higher energy levels because of absorption of energy. When these electrons return to their ground states, they emit extra energy in form of radiations which fall in the visible region thereby imparting a characteristic colour to the flame.
Ba and Mg do not impart any colour to the fame i.e. they do not give flame test. This is due to their very small size. Ca, Sr and Ba impart brick red, Blood red and Apple green colours respectively to the flame.

When alkalike metals are heated on a Bunsen flame the electrons get excited to higher energy level due to taking in of energy. When these electrons return to ground state they emit the extra energy in form if radiations which are are in the visibility spectrum hence we can see a flame colour for each of themHowever no charactoristic colour is shown by magnesium or berrilyium since their atoms have a smaller size and due to small size the nuclear charge experienced by the electrons is greater. Therefore greater amount of energy is needed for excitation of electron to higher energy level which is not provided by the buns end flame.

Be and Mg are smaller in size and their electron are strongly bound to the nucleus . They need large amount of energy for excitation of electrons to higher energy level which is not available in Bunsen flame , so they do not impart colour to the flame.