Q.What happens when

1. Sodium metal dropped in water Sodium reacts vigorously and exothermically with cold water, liberating hydrogen gas:

   $2Na + 2H_2O \rightarrow 2NaOH + H_2\uparrow$

   The heat released can be enough to melt the sodium into a molten globule and, in some cases, ignite the liberated hydrogen.
2. Sodium metal heated in a free supply of air When freely supplied with (excess) air/oxygen and heated, sodium burns to form sodium peroxide (with some normal oxide also present):

   $2Na + O_2 \xrightarrow{\Delta} Na_2O_2$

3. Sodium peroxide dissolving in water Sodium peroxide reacts with water to regenerate sodium hydroxide and hydrogen peroxide: …

Recall the three canonical sodium reactions independently: vigorous hydrolysis of the metal in cold water, oxidation to the peroxide (not the simple oxide) when heated in a generous air/ …

• Writing Na$_2$O (simple oxide) as the product of burning Na in air instead of Na$_2$O$_2$ (peroxide), which forms preferentially in a free/excess supply of air/oxygen.
• Missing hydrogen peroxide as a product when Na$_2$O$_2$ reacts with water, and writing only NaOH + O$_2$ instead of NaOH + H$_2$O$_2$. …