Question
while going down the second group, the reactivity of the alkaline earth metals increases.

Answer

The reaction of alkaline earth metal with water is $M +2 H _2 O \rightarrow M ( OH )_2+ H _2$. while going down the second group as $Be \rightarrow Mg \rightarrow Ca \rightarrow Sr \rightarrow Ba$, the gradation in this chemical property or the alkaline earth metals is seen. while going down the second group the reactivity of the alkaline earth metals goes on increasing thereby the ease with which this reaction takes place also goes on increasing.
Thus, Beryllium (Be) does not react with water. Mg (Magnesium) reacts with steam. whereas calcium (Ca), strontium (Sr) and barimm (Ba) reacts with water at room temperature with increasing rates.

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