The hydrogen spectrum refers to the series of spectral lines produced when the electrons in a hydrogen atom transition from higher energy levels to lower energy levels. These transitions result in the emission or absorption of photons, which are particles of light with specific wavelengths.

Ultraviolet Region:
The ultraviolet region of the hydrogen spectrum corresponds to transitions from higher energy levels to the ground state (n=1). The largest wavelength in this region is given as 122 nm.

Infrared Region:
The infrared region of the hydrogen spectrum corresponds to transitions from higher energy levels to the excited states (n>1). The smallest wavelength in this region can be determined by finding the transition from the highest energy level to the lowest excited state.

Finding the Smallest Wavelength:
The energy levels in hydrogen are given by the formula E = -13.6/n^2 eV, where n is the principal quantum number. To find the highest energy level, we need to find the largest value of n.

By setting the energy equal to zero (since the ionization energy is zero at infinity), we can solve for n:
0 = -13.6/n^2
n^2 = 13.6
n ≈ 3.7

Since n must be an integer, the highest energy level is n = 4.

To find the lowest excited state, we need to find the transition from the highest energy level to the next lowest energy level. This transition corresponds to n=4 to n=3.

Using the formula for calculating the wavelength of light emitted or absorbed during a transition in the hydrogen spectrum (1/λ = R(1/n1^2 - 1/n2^2)), where R is the Rydberg constant, we can find the wavelength.

Plugging in the values, we get:
1/λ = R(1/4^2 - 1/3^2)
1/λ = R(1/16 - 1/9)
1/λ = R(9 - 16)/144
1/λ = -7R/144
λ = -144/7R

The value of the Rydberg constant is approximately 1.097 × 10^7 m^-1. Plugging this value in, we find:
λ ≈ -144/7(1.097 × 10^7)
λ ≈ -18.21 nm

Since we are looking for the smallest wavelength in the infrared region, we take the absolute value:
λ ≈ 18.21 nm

Rounding this to the nearest integer, we get 18 nm, which is the smallest wavelength in the infrared region.

Therefore, the correct answer is '823'.