Prussian blue is not the sodium salt that forms first — it appears only once that sodium salt meets iron in the +$\displaystyle 3$ state, giving the compound \(\displaystyle \text{Fe}_4[\text{Fe(CN)}_6]_3\). Track the iron and the cyanide through each step of the test and the answer falls out of the bookkeeping.
Step $\displaystyle 1$ — sodium fusion makes cyanide, not any iron compound yet.
When the nitrogen-containing organic compound is fused with sodium metal, its carbon and nitrogen atoms combine with sodium to give sodium cyanide in the fusion extract:
\[\text{Na} + \text{C} + \text{N} \longrightarrow \text{NaCN}
\]
There is no iron anywhere in this step — the extract is just a solution containing \(\displaystyle \text{Na}^+\) and \(\displaystyle \text{CN}^-\) (plus \(\displaystyle \text{NaOH}\), \(\displaystyle \text{Na}_2\text{S}\), etc., from other elements). Iron is added only in the next step, so option (a), which already has iron in it, cannot be what forms here.
Step $\displaystyle 2$ — boiling with FeSO₄ builds the ferrocyanide ion.
The alkaline extract is boiled with freshly prepared iron(II) sulphate, \(\displaystyle \text{FeSO}_4\) (iron here is \(\displaystyle \text{Fe}^{2+}\), the ferrous state). Excess \(\displaystyle \text{CN}^-\) wraps around each \(\displaystyle \text{Fe}^{2+}\) to give the complex hexacyanidoferrate(II) ion, isolated as sodium ferrocyanide:
\[\text{FeSO}_4 + 6\,\text{NaCN} \longrightarrow \text{Na}_4[\text{Fe(CN)}_6] + \text{Na}_2\text{SO}_4
\]
Check the balance: iron, \(\displaystyle 1=1\); sodium, \(\displaystyle 6\) on the left equals \(\displaystyle 4+2\) on the right; \(\displaystyle \text{CN}\), \(\displaystyle 6=6\); sulphate, \(\displaystyle 1=1\). In \(\displaystyle \text{Na}_4[\text{Fe(CN)}_6]\) the iron is still \(\displaystyle \text{Fe}^{2+}\) — this is option (a). It is pale/colourless in solution, not blue, because the blue colour needs a
second, higher oxidation state of iron to react with it. This is the step people stop at and wrongly pick (a): forming \(\displaystyle \text{Na}_4[\text{Fe(CN)}_6]\) is necessary for the test, but it is an intermediate, not the coloured product asked for.
Step $\displaystyle 3$ — some iron is already Fe³⁺.
\(\displaystyle \text{FeSO}_4\) solution is never perfectly pure \(\displaystyle \text{Fe}^{2+}\); air oxidises part of it to iron(III) sulphate on standing and boiling, so the mixture always carries some \(\displaystyle \text{Fe}^{3+}\) alongside the \(\displaystyle \text{Fe}^{2+}\) that became ferrocyanide.
Step $\displaystyle 4$ — acidifying brings Fe³⁺ and ferrocyanide together, and that reaction is Prussian blue.
On cooling and acidifying with dilute sulphuric acid, any iron hydroxide precipitate dissolves back into solution as \(\displaystyle \text{Fe}^{3+}\), and these ferric ions combine with the sodium ferrocyanide made in Step $\displaystyle 2$ to throw down an intensely coloured, insoluble precipitate:
\[3\,\text{Na}_4[\text{Fe(CN)}_6] + 2\,\text{Fe}_2(\text{SO}_4)_3 \longrightarrow \text{Fe}_4[\text{Fe(CN)}_6]_3 + 6\,\text{Na}_2\text{SO}_4
\]
Balance check: sodium, \(\displaystyle 12=12\); iron, \(\displaystyle 3\) (inside the three ferrocyanide units) \(\displaystyle +\,4\) (from the ferric sulphate) \(\displaystyle =7\) on the left, and on the right \(\displaystyle 4\) (outside) \(\displaystyle +\,3\) (inside) \(\displaystyle =7\); \(\displaystyle \text{CN}\), \(\displaystyle 18=18\); sulphate, \(\displaystyle 6=6\).
The product, \(\displaystyle \text{Fe}_4[\text{Fe(CN)}_6]_3\), in words is
ferric ferrocyanide (iron(III) hexacyanidoferrate(II)) — this is exactly Prussian blue. Its charges make sense with real oxidation states: the four outer iron atoms are \(\displaystyle \text{Fe}^{3+}\) (\(\displaystyle 4\times(+3)=+12\)), and each \(\displaystyle [\text{Fe(CN)}_6]\) unit inside carries the inner iron as \(\displaystyle \text{Fe}^{2+}\) with a \(\displaystyle 4-\) charge (three units give \(\displaystyle 3\times(-4)=-12\)), so the compound is neutral — a genuine, stable substance.
Aside — why the other options fail on this same charge check. Option (c), \(\displaystyle \text{Fe}_2[\text{Fe(CN)}_6]\), would need the
outer iron to also be \(\displaystyle \text{Fe}^{2+}\) (ferrous), giving \(\displaystyle 2\times(+2)=+4\) against the ferrocyanide's \(\displaystyle -4\) — this is a real compound (ferrous ferrocyanide, pale/white, not blue), but it needs Fe²⁺ everywhere, and this test always oxidises some iron to Fe³⁺, so it isn't what forms in the Prussian-blue step. Option (d), \(\displaystyle \text{Fe}_3[\text{Fe(CN)}_6]_4\), does not even balance charge for any simple oxidation state: \(\displaystyle 3\times(+3)=+9\) against \(\displaystyle 4\times(-4)=-16\) — the numbers don't match, so this is not a real product of the reaction at all.
Answer: (b) \(\displaystyle \text{Fe}_4[\text{Fe(CN)}_6]_3\) — ferric ferrocyanide, the Prussian blue compound.