Question

The hydrogen atom can give spectral lines in the series Lyman, Balmer and Paschen. which of the following statement is correct (A) Lyman series is in the infrared region (B) Balmer series is in the ultraviolet region (C) Balmer series is in the visible region (D) Paschen series is in the visible region.

Short answer

The correct statement is (C) Balmer series is in the visible region.

Step-by-step solution

Spectral Series of Hydrogen Atom

The hydrogen atom has a series of spectral lines known as the Lyman, Balmer, and Paschen series. Each series corresponds to the transitions of an electron between energy levels in the hydrogen atom as it emits or absorbs photons. The wavelengths of these spectral lines are 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 specific to the hydrogen atom, \(\lambda\) is the wavelength of the spectral line, and \(n_1\) and \(n_2\) are the principal quantum numbers of the electron energy levels involved in the transition. For the Lyman series, the transitions have \(n_1 = 1\), and for the Balmer series, \(n_1 = 2\), while for the Paschen series, \(n_1 = 3\). The \(n_2\) values can range from \(n_1 + 1\) to infinity. Now, let's check the regions in which these series lie in the electromagnetic spectrum.

Regions in Electromagnetic Spectrum

The electromagnetic spectrum is divided into several regions, some of which are ultraviolet (UV), visible, and infrared (IR). The approximate wavelength ranges for these regions are: - Ultraviolet: 10 nm to 400 nm - Visible: 400 nm to 700 nm - Infrared: 700 nm to 1 mm Using the Rydberg formula for each series, we can determine the approximate wavelength range and which region of the electromagnetic spectrum they fall into.

Checking Each Statement

(A) Lyman series is in the infrared region: By choosing \(n_1 = 1\) and varying \(n_2\), we get the wavelength range as 10 nm to 122 nm, which falls in the ultraviolet region. Therefore, this statement is FALSE. (B) Balmer series is in the ultraviolet region: By choosing \(n_1 = 2\) and varying \(n_2\), the range of Balmer series is approximately 365 nm to 656 nm, which falls within the visible light region. This statement is FALSE. (C) Balmer series is in the visible region: As we stated in option (B), the Balmer series wavelength range falls within the visible light region. Therefore, this statement is TRUE. (D) Paschen series is in the visible region: By setting \(n_1 = 3\) and varying \(n_2\), we find that the wavelength range for the Paschen series is approximately 820 nm to 1875 nm, which falls into the infrared region. This statement is FALSE. Based on the analysis, the correct statement is (C) Balmer series is in the visible region.