Why do beryllium and magnesium not impart colour to the flame in the flame test?

(N/A) Except $Be$ and $Mg$,all alkaline earth metals impart characteristic colours to the flame of a Bunsen burner.
These two metals have very small atomic radii,and their electrons are more strongly bound due to a high effective nuclear charge.
The energy provided by the Bunsen flame is not sufficient to excite these electrons to higher energy levels.
Hence,these elements do not impart any colour to the flame.