[UPSC IFoS 2019] Molecular Physics (Q193, 8M)

The first rotational line of ^{12}\text{C}^{16}\text{O} is observed at 3\cdot 84235~\text{cm}^{-1} and that of ^{13}\text{C}^{16}\text{O} at 3\cdot 67337~\text{cm}^{-1}. Assuming the mass of ^{16}\text{O} to be 15\cdot 9949~\text{u}, calculate that of ^{13}\text{C}.