Question

Explain the reason, according to Bohr’s atomic model, why atomic emission spectra contain only certain frequencies of light.

Short answer

According to Bohr's atomic model, electrons in an atom can only exist in specific energy levels or orbits. When electrons transition between these quantized energy levels, they emit or absorb energy in the form of light. The energy difference during a transition, \(ΔE\), is related to the frequency of the emitted light through the equation \(ΔE = hν\), where \(h\) is Planck's constant and \(ν\) is the frequency of the emitted light. This implies that only specific frequencies of light can be emitted during electron transitions. Thus, atomic emission spectra contain only certain discrete frequencies of light, corresponding to the energy differences between the specific energy levels in an atom.

Step-by-step solution

Recall Bohr's atomic model

Bohr's atomic model describes the behavior of electrons in an atom. According to this model, electrons can only exist in specific energy levels, also known as "orbits" or "shells", around the nucleus of an atom. An electron can move from one energy level to another, but it cannot exist between these energy levels.

Understand the transition of electrons between energy levels

When energy is provided to an electron in an atom, the electron can get excited and jump from a lower energy level to a higher energy level. This process is called "excitation". Similarly, when an electron moves from a higher energy level to a lower energy level, it releases energy in the form of light, through a process called "de-excitation" or "relaxation".

Calculate the energy difference during a transition

The energy difference between the initial and final energy levels during a transition is given by the following formula: ΔE = E_final - E_initial where ΔE is the energy difference, and E_final and E_initial are the final and initial energy levels, respectively.

Relate the energy difference to the frequency of emitted light

The energy difference during a transition is directly related to the frequency of the emitted light, according to the following equation: \(ΔE = hν\) where h is Planck's constant (\(6.626 × 10^{-34}~J·s\)), ν (nu) is the frequency of the emitted light, and ΔE is the energy difference between the two energy levels. This equation implies that only specific frequencies of light can be emitted during these electron transitions, since the energy levels are quantized.

Connect the concept to atomic emission spectra

Atomic emission spectra represent the wavelengths or frequencies of light emitted by atoms when their electrons undergo transitions between energy levels. Since Bohr's atomic model describes that electrons can only exist in specific, quantized energy levels, the frequency of light emitted during these transitions is also quantized. This means that atomic emission spectra contain only certain discrete frequencies of light, corresponding to the energy differences between the specific energy levels in an atom.

Key concepts

Atomic Emission Spectra

The atomic emission spectrum is a fascinating display of colors that is unique to each element, like a fingerprint. When an atom's electrons drop from a higher to a lower energy level, they emit light, creating this beautiful spectrum. Each element can only emit light at specific frequencies.
Therefore, when we observe the atomic emission spectrum, we see discrete lines, each corresponding to a particular frequency of light.
This is because these frequencies relate directly to the energy changes as electrons move between energy levels. For a more accurate visualization, you can think of the spectrum as a series of bright lines on a dark background, each line representing a specific frequency of light emitted by electrons as they transition back to lower energies.

Electron Energy Levels

In Bohr's atomic model, electrons exist in fixed energy levels around a nucleus. These levels are sometimes referred to as orbits or shells.
An electron must occupy one of these levels, and it cannot exist between them. Picture these energy levels like rungs of a ladder. Electrons can only "stand" on the rungs, not in between them.
The arrangement of these energy levels is crucial because it dictates the energy an electron needs to jump from one level to another. This ladder-like structure of energy levels is what enables the unique emission spectra of different elements.

Quantized Energy

Quantized energy means that the energy levels in an atom are fixed and distinct. In other words, electrons can only have certain specific amounts of energy.
Just like climbing stairs, where you can only stand on separate steps, not in between them, electrons jump between distinct energy levels.
This step-like energy arrangement is crucial because it ensures that only specific energies can be absorbed or emitted by electrons. This is the heart of how atomic spectra arise since each jump from one level to another corresponds to a unique energy change.

Excitation and De-Excitation

Excitation and de-excitation are processes that involve electrons moving between energy levels. Excitation occurs when an electron absorbs energy and jumps to a higher energy level.

• This is like gaining enough energy to reach a higher rung on the ladder of energy states.
• Conversely, de-excitation happens when electrons return to a lower energy level, releasing energy in the form of light.
• The color or frequency of this light depends on the energy difference between the levels.

Understanding these processes helps explain the discrete frequencies seen in atomic emission spectra.

Planck's Constant

Planck's constant is a fundamental quantity in quantum mechanics, denoted by the symbol \( h \). It connects the energy of a photon (a particle of light) to its frequency according to the formula \( E = hu \), where \( E \) is the energy, \( h \) is Planck's constant, and \( u \) is the frequency.
With a value of approximately \( 6.626 \times 10^{-34} \text{ J·s} \), Planck's constant plays a crucial role in explaining why energy levels are quantized within an atom. It shows how even the smallest quantities of energy relate to frequency, underpinning key aspects of Bohr’s atomic model and atomic emission spectra.
By studying Planck's constant, we understand the quantized nature of light and energy at a microscopic scale, fundamental in modern physics.