How can I write the formula for potassium nitride?

Hint: Potassium nitride is an inorganic compound and ionic salt of potassium and nitrate ions which further form a white or light yellow colored hygroscopic crystalline powder which is soluble in water. It acts as a strong oxidizer.

Complete answer:
To know about the formula of potassium nitride we first know about the electronic configuration of potassium represented by symbol $K$ and nitrogen represented by the symbol $N$.
Now we know that atomic number of $K$ is 19 so electronic configuration can be written as: $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{1}}$. As potassium obeys the octet rule therefore it will lose one electron from its $4s$ subshell to achieve a stable octet known as noble gas configuration by forming the cation represented by the symbol ${{K}^{+}}$ and electronic configuration of ${{K}^{+}}$ is given by $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}$.
Now we know that nitrogen atom has seven electrons and the electronic configuration of nitrogen atom can be written as: $1{{s}^{2}}2{{s}^{2}}2{{p}^{3}}$. Like potassium nitrogen will also obeys the octet rule and as a result it will gain three electrons to achieve stable octet called noble gas configuration which forms anion i.e. negative nitride ion represented by the symbol ${{N}^{3-}}$ and electronic configuration of ${{N}^{3-}}$ can be written as: $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}$.
From this we can consider that each nitrogen atom gains three electrons from three potassium atoms and each potassium atom loses one electron from a nitrogen atom. So the formula of potassium nitride can be written as ${{K}_{3}}N$.

Note:
Potassium nitrite is mainly used as a medicinal purpose and also used in the manufacturing of heat transfer salts, as food additive or preservative. It is very much reactive in nature like when it reacts with reducing agents it causes fires and explosions.