MCAT Expertise
Note that all systems tend toward minimal energy; thus on the MCAT, atoms of any element will generally exist in the ground state unless subjected to extremely high temperatures or irradiation.
APPLICATIONS OF THE BOHR MODEL
The Bohr model of the hydrogen atom (and other one-electron systems, such as He+ and Li2+) is useful for explaining the atomic emission spectrum and atomic absorption spectrum of hydrogen, and it is helpful in the interpretation of the spectra of other atoms.
Atomic Emission Spectra
At room temperature, the majority of atoms in a sample are in the ground state. However, electrons can be excited to higher energy levels by heat or other energy forms to yield the excited state of the atom. Because the lifetime of the excited state is brief, the electrons will return rapidly to the ground state, resulting in the emission of discrete amounts of energy in the form of photons. The electromagnetic energy of these photons can be determined using the following equation:
where h is Planck’s constant, c is the speed of light in a vacuum (3.00 × 108 m/s), and
Bridge
E = hf for photons in physics. This also holds true here because we know that c = f
The different electrons in an atom can be excited to different energy levels. When these electrons return to their ground states, each will emit a photon with a wavelength characteristic of the specific energy transition it undergoes. The quantized energies of light emitted under these conditions do not produce a continuous spectrum (as expected from classical physics). Rather, the spectrum is composed of light at specified frequencies and is thus known as a line spectrum, where each line on the emission spectrum corresponds to a specific electronic transition. Because each element can have its electrons excited to different distinct energy levels, each one possesses a unique atomic emission spectrum, which can be used as a fingerprint for the element. One particular application of atomic emission spectroscopy is in the analysis of stars and planets: While a physical sample may be impossible to procure, the light from a star can be resolved into its component wavelengths, which are then matched to the known line spectra of the elements.
Real World
Emissions from electrons in molecules, or atoms dropping from an excited state to a ground state, give rise to fluorescence. We see the color of the emitted light.
The Bohr model of the hydrogen atom explained the atomic emission spectrum of hydrogen, which is the simplest emission spectrum among all the elements. The group of hydrogen emission lines corresponding to transitions from the upper energy levels n > 2 to n = 2 (that is to say, the pattern of photon emissions from the electron falling from the n > 2 energy level to the n = 2 energy level) is known as the Balmer series and includes four wavelengths in the visible region. The group corresponding to transitions from the upper levels n > 1 to n = 1 (that is to say, the emissions of photons from the electron falling from the higher energy levels to the ground state) is called the Lyman series, which includes larger energy transitions and therefore shorter photon wavelengths in the UV region of the electromagnetic spectrum.
When the energy of each frequency of light observed in the emission spectrum of hydrogen was calculated according to Planck’s quantum theory, the values obtained closely matched those expected from energy level transitions in the Bohr model. That is, the energy associated with a change in the quantum number from an initial higher value ni to a final lower value nf is equal to the energy of the photon predicted by Planck’s quantum theory. Combining Bohr’s and Planck’s calculations, we arrive at
The energy of the emitted photon corresponds to the precise difference in energy between the higher-energy initial state and the lower-energy final state.
Atomic Absorption Spectra
When an electron is excited to a higher energy level, it must absorb energy. The energy absorbed that enables an electron to jump from a lower-energy level to a higher one is characteristic of that transition. This means that the excitation of electrons in the atoms of a particular element results in energy absorption at specific wavelengths. Thus, in addition to a unique emission spectrum, every element possesses a characteristic absorption spectrum. Not surprisingly, the wavelengths of absorption correspond directly to the wavelengths of emission because the difference in energy between levels remains unchanged. Identification of elements present in a gas phase sample requires absorption spectra.
Real World
Absorption is the basis for color of compounds. We see the color of the light that is NOT absorbed by the compound.
You’ve just been put through a series of paragraphs crammed with technical language (mumbo jumbo is too strong a term; after all, you are sufficiently intelligent to grasp these concepts). That said, at least a few pairs of eyes reading this book will have gone glassy by this point. Therefore, let’s bring this back to the realm of experience by way of analogy. We’ve already discussed equating the energy levels available to electrons to stairs on a staircase. Taking this analogy one step further, so to speak: Let’s imagine that you and your friend are walking side-by-side up a set of stairs. You have very long legs, so it is your habit to take two, sometimes even three, steps at a time; your friend has short legs and so takes one, or at most two, steps at a time. The pattern by which you jump from a lower step to a higher one will be characteristic to you and you alone and will be quite different from the pattern by which your friend jumps from a lower step to a higher one, which will be unique to her. Furthermore, you have to invest energy into the process of ascending the staircase. This in a nutshell is the significance of the atomic absorption spectrum. The atomic emission spectrum is simply a record of the process in reverse.
MCAT Expertise
ΔE is the same for absorption or emission between any two energy levels. The sign (positive or negative) of ΔE indicates whether the energy goes in or out and, therefore, whether the electron is going to an excited state (absorption) or to the ground state (emission), respectively.