 Solution

Anharmonicity places the $1\to 2$ hot band atonly $3.7\mathrm{c}{\mathrm{m}}^{-1}$ below the fundamental. It can be detected with adequate spectral resolution and signal-to-noise; it is not guaranteed to appear as a separate peak in an unresolved band contour. The predicted ten-percent population-based intensity is appreciable, but overlapping rotational branches and linewidth can hide it beneath the stronger fundamental. No instrumental resolution or linewidth is supplied, so an unconditional assertion of visibility or invisibility would go beyond the information given.