Learning Outcomes
By the end of this lesson, students will be able to:
i. Describe the spectrum of hydrogen, recognizing that it consists of a series of discrete lines representing transitions between energy levels in the hydrogen atom.
ii. Correlate the spectral lines of hydrogen with the mathematical expressions derived in Lesson 3, understanding the relationship between the wavelength of emitted light and the energy difference between electron energy levels.
iii. Calculate the wavelengths of emitted light for different transitions in the hydrogen atom, applying the Bohr model and the Rydberg constant.
iv. Explain the Lyman series, Balmer series, Paschen series, and Brackett series, recognizing that these series represent transitions between specific energy levels in the hydrogen atom.
v. Appreciate the significance of the hydrogen spectrum in validating the Bohr model, understanding that the observed emission lines align with the predicted energy transitions.
Introduction
The hydrogen atom, with its single electron and relatively simple structure, serves as an ideal model for exploring the relationship between atomic structure and spectral emission. When subjected to an electrical discharge, hydrogen atoms emit light, producing a characteristic spectrum consisting of discrete lines. These lines represent transitions between different energy levels of the electron within the hydrogen atom.
i. A Spectrum of Energy Transitions
The spectrum of hydrogen, unlike the continuous spectra of incandescent solids or liquids, consists of a series of discrete lines, each corresponding to a specific energy transition of the electron. These lines appear at distinct wavelengths, ranging from the ultraviolet to the infrared regions of the electromagnetic spectrum.
ii. Correlating Lines and Energy Levels
The wavelengths of the spectral lines of hydrogen can be calculated using the Bohr model equation for the energy of an electron:
E_n = -13.6 eV/n^2
where:
E_n is the energy of an electron in the nth energy level
n is the principal quantum number, representing the energy level
By taking the energy difference between the initial and final energy levels involved in a transition, the frequency (ν) of the emitted light can be determined using the relationship:
ν = (E_i - E_f)/h
where:
ν is the frequency of emitted light
E_i is the energy of the electron in the initial energy level (n_i)
E_f is the energy of the electron in the final energy level (n_f)
h is Planck's constant
Finally, the wavelength (λ) of the emitted light can be calculated using the equation:
λ = c/ν
where:
λ is the wavelength of emitted light
c is the speed of light in a vacuum
ν is the frequency of emitted light
iii. Spectral Series: A Signature of Energy Transitions
The spectral lines of hydrogen can be grouped into four series: the Lyman series, the Balmer series, the Paschen series, and the Brackett series. Each series represents transitions between specific energy levels within the hydrogen atom.
The Lyman series corresponds to transitions from higher energy levels (n > 1) to the first energy level (n = 1). These lines fall in the ultraviolet region of the spectrum.
The Balmer series corresponds to transitions from higher energy levels (n > 2) to the second energy level (n = 2). These lines are visible in the red and blue regions of the spectrum.
The Paschen series corresponds to transitions from higher energy levels (n > 3) to the third energy level (n = 3). These lines lie in the infrared region of the spectrum.
The Brackett series corresponds to transitions from higher energy levels (n > 4) to the fourth energy level (n = 4). These lines also fall in the infrared region of the spectrum.
iv. Validating the Bohr Model: A Triumph of Theory
The observation of the discrete spectral lines of hydrogen provided compelling evidence for the Bohr model of the atom. The wavelengths of the observed lines matched remarkably well with those predicted by the model, confirming the existence of quantized energy levels within the hydrogen atom.
The spectrum of hydrogen serves as a testament to the power of the Bohr model in explaining the structure of the atom and the relationship between atomic structure and spectral emission. By analyzing the discrete lines in the hydrogen spectrum, scientists have gained valuable insights into the quantized energy levels of electrons within atoms and the energy transitions that give rise to the emission of light.
