Kaplan MCAT General Chemistry Review

Bohr came to describe the structure of the hydrogen atom as a nucleus with one proton forming a dense core around which a single electron revolved in a defined pathway of a discrete energy value. Transferring an amount of energy exactly equal to the difference in energy between one pathway, or orbit, and another, resulted in the electron “jumping” from one pathway to a higher energy one. These pathways or orbits had increasing radii, and the orbit with the smallest radius in which hydrogen’s electron could be found was called the ground state and corresponded to n = 1. When the electron was promoted to a higher energy orbit (one with a larger radius), the atom was said to be in the excited state. Bohr likened his model of the hydrogen atom to the planets orbiting the sun, in which each planet traveled along a (roughly) circular pathway at set distances (and energy values) with respect to the sun. In spite of the fact that Bohr’s model of the atom was overturned within the span of two decades, he was awarded the Nobel Prize in Physics in 1922 for his work on the structure of the atom and to this day is considered one of the greatest scientists of the 20th century.

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 is the wavelength of the radiation.

Bridge

E = hf for photons in physics. This also holds true here because we know that c = f. This is based on the formula v = f for photons.

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.