Red phosphorus, when heated in a sealed tube at 803 K, gives 'X'. White phosphorus, when heated under high pressure at 473 K, gives 'Y'. X, Y respectively are
Step 1: Formation of $\alpha$-Black Phosphorus:
It is formed when Red Phosphorus is heated in a sealed tube at 803 K. It can be sublimed in air and has opaque monoclinic or rhombohedral crystals. So, $X = \alpha$-Black Phosphorus.
Step 2: Formation of $\beta$-Black Phosphorus:
It is prepared by heating White Phosphorus at 473 K under high pressure. So, $Y = \beta$-Black Phosphorus.
Step 3: Final Answer:
X is $\alpha$-Black phosphorus and Y is $\beta$-Black phosphorus.