Kaplan MCAT General Chemistry Review

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 n_i to a final lower value n_f 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.

Quantum Mechanical Model of Atoms