Final answer:
The correct answer is option C. 1882 nm.
Step-by-step explanation:
The hydrogen spectrum consists of various series of spectral lines that have been observed in the infrared (IR), visible, and ultraviolet (UV) regions.
The largest wavelength in the ultraviolet region of the hydrogen spectrum is given as 122 nm.
The smallest wavelength in the infrared region of the hydrogen spectrum can be calculated using the formula provided, which gives us a value of approximately 1882 nm.
Therefore, the correct answer is option C. 1882 nm.