Final answer:
The wavelength of the first line in the Lyman series can be calculated using the Rydberg formula. By applying this to the transition from n=2 to n=1 and using the Rydberg constant, we find that the wavelength falls in the UV region, confirming that the first line in the Lyman series is UV radiation.
The correct answer is options a) True.
Step-by-step explanation:
To determine if the first line in the Lyman series of hydrogen is UV radiation, we use the formula derived from Bohr's Theory of the Hydrogen Atom. The Lyman series corresponds to electronic transitions from higher energy levels to the ground state (n=1) of the hydrogen atom.
Based on Bohr's model, the wavelength (λ) of emitted radiation can be calculated using the Rydberg formula:
Rydberg formula: 1/λ = R_H (1/n_1^2 - 1/n_2^2)
For the first line of the Lyman series, the transition is from n=2 to n=1:
1/λ = R_H (1/1^2 - 1/2^2) = R_H (1 - 1/4) = R_H * 3/4
R_H is the Rydberg constant (approximately 1.097 x 10^7 m^-1).
λ = 1 / (R_H * 3/4)
After calculating λ, we find that the wavelength falls in the ultraviolet (UV) region, verifying that the first line in the Lyman series is indeed UV radiation. The exact wavelength can be determined by substituting the value of R_H into the formula.
The correct answer is options a) True.