1/l=R(1/n22-1/n­12)
=>1/122=R(1-1/4)
=>1/122=3R/4
=>R=4/3x122

smallest l in the infrared region. n1= infinity
n2=3
Therefore, 1/l = R(1/32-1/infinity)
=R/9
l=9/R=823nm.

Ultraviolet Region of the Hydrogen Spectrum
The hydrogen spectrum consists of a series of lines that are produced when the electrons in hydrogen atoms transition between different energy levels. These transitions correspond to the emission or absorption of photons with specific wavelengths.

In the ultraviolet region of the hydrogen spectrum, the transitions involve higher energy levels. The largest wavelength in this region corresponds to the transition from the highest energy level to the second energy level.

Largest Wavelength in the Ultraviolet Region
Given that the largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm, we need to find the energy level transition that corresponds to this wavelength.

Using the Rydberg formula, which relates the wavelength of a spectral line to the energy levels involved, we can calculate the transition.

1/λ = R_H * (1/n₁² - 1/n₂²)

Where:
λ is the wavelength
R_H is the Rydberg constant for hydrogen (approximately 1.097 x 10^7 m⁻¹)
n₁ and n₂ are the principal quantum numbers for the initial and final energy levels, respectively.

Since we are looking for the largest wavelength, the transition must involve the highest energy level. Therefore, n₁ = 1 and n₂ = ∞ (infinity).

1/λ = R_H * (1/1² - 1/∞²)
1/λ = R_H * (1/1 - 0)
1/λ = R_H

Solving for λ, we find:
λ = 1/R_H

Substituting the value of the Rydberg constant:
λ = 1/(1.097 x 10^7 m⁻¹)

Converting meters to nanometers:
λ ≈ 91 nm

Therefore, the largest wavelength in the ultraviolet region of the hydrogen spectrum is approximately 91 nm, which is different from the given value of 122 nm.

Infrared Region of the Hydrogen Spectrum
In the infrared region of the hydrogen spectrum, the transitions involve lower energy levels. The smallest wavelength in this region corresponds to the transition from the second energy level to the lowest energy level.

Smallest Wavelength in the Infrared Region
To find the smallest wavelength in the infrared region, we can use the same approach as before.

1/λ = R_H * (1/n₁² - 1/n₂²)

For the smallest wavelength, the transition must involve the second energy level (n₁ = 2) and the lowest energy level (n₂ = 1).

1/λ = R_H * (1/2² - 1/1²)
1/λ = R_H * (1/4 - 1)
1/λ = -3R_H/4

Solving for λ, we find:
λ = -4/3R_H

Substituting the value of the Rydberg constant:
λ = -4/3(1.097 x 10^7 m⁻¹)

Converting meters to nanometers and taking the absolute value:
λ ≈ 823 nm

Therefore, the smallest wavelength in the infrared region of the hydrogen spectrum is approximately 823 nm, which matches option B.