Question

Introduction: When an electron absorbs a photon, it gains energy. The added energy causes the electron to move to an orbit that is farther from the nucleus. Because each possible orbit is associated with a particular amount of energy, orbits are known as energy levels.

By convention, an energy of 0 eV is assigned to the energy level that is infinitely far from the nucleus. (This is done so that atoms of different elements can be compared from a common starting point.) As a result of this convention, each energy level has a negative energy.
Question: How do energy levels relate to the spectrum of hydrogen?
List: Look at the graph of energy levels.
List the energy of each level (n = 1, 2, 3, etc.)

Answer 1

The energy levels in a hydrogen atom correlate with the atomic emission spectra through the quantized transitions of electrons between these levels. Each energy level has a specific energy value, and when an electron jumps between these levels, photons with specific frequencies are either absorbed or emitted, forming the characteristic hydrogen spectrum.

Step-by-step explanation:

Energy levels in a hydrogen atom are significant because they are related to the atomic emission spectra observed. Each energy level of an electron within the hydrogen atom has a specific, quantized energy value and is indexed by a quantum number, n. The ground state of hydrogen, or the state of lowest energy, is denoted by n = 1 and has an energy of -13.6 eV. As the electron gains energy, it can move to higher energy levels, such as n = 2 or n = 3, with less negative energy values like -3.4 eV and -1.5 eV respectively. When an electron transitions between these discrete energy levels, it either absorbs or emits a photon with an energy equal to the difference between the initial and final energy levels, giving rise to a spectrum of radiation with specific wavelengths characteristic of hydrogen.

Transitioning from a lower energy level to a higher one requires the absorption of energy, usually from a photon, and results in an excited state. Conversely, when an electron falls back to a lower energy level, it emits a photon, contributing to the formation of spectral lines. These spectral lines appear at certain frequencies and correspond to the jumps between specific energy levels. Thus, the spectral lines we observe in the hydrogen spectrum are the visual manifestation of these energy transitions.

For example, when an electron in hydrogen transitions from n = 2 to n = 3, it absorbs a photon, increasing its energy. When the electron returns to a lower energy state, such as going from n = 3 back to n = 1, it emits a photon. The frequency of the absorbed or emitted photon can be calculated using the energy difference between the levels and is predicted by Planck's formula E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. These processes generate atomic emission spectra, which are characteristic for each element.