The Lyman series of hydrogen atom lies in the ultraviolet region of the electromagnetic spectrum. The Lyman series is a series of spectral lines in the hydrogen atom that are produced when an electron falls from an excited state to the n=1 (ground) state. The wavelength of the light emitted in a transition is given by the Rydberg formula:
$$\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} – \frac{1}{n_2^2}\right)$$
where $R_H$ is the Rydberg
constant and $n_1$ and $n_2$ are the principal quantum numbers of the initial and final states, respectively. The Lyman series corresponds to transitions from $n_2 = 2, 3, 4, …$ to $n_1 = 1$. The shortest wavelength in the Lyman series is for the transition from $n_2 = 2$ to $n_1 = 1$, which has a wavelength of 121.6 nm. This wavelength is in the ultraviolet region of the electromagnetic spectrum.The other options are incorrect because they do not correspond to the Lyman series. The visible region of the electromagnetic spectrum corresponds to wavelengths of 380-700 nm. The infrared region of the electromagnetic spectrum corresponds to wavelengths of 700-1000 nm. The X-ray region of the electromagnetic spectrum corresponds to wavelengths of 0.01-10 nm.