M A. B. Figure 3 - Diagram of two waves. Which is of higher energy, wave " $$ A $$ " or wave " $$ B $$ "? $$ \qquad $$ How do atoms produce visible light and how is it related to atomic structure? The current model of atomic structure includes the presence of a nucleus (consisting of protons and neutrons) surrounded by electrons. Experimental evidence, including the analysis of light emitted from excited atoms, has led to the hypothesis that electrons in an atom exist at certain allowable locations away from the nucleus, corresponding to certain energy states or energy levels. Electrons closer to the nucleus are considered to be lower in energy than those further from the nucleus. Electrons can absorb energy from a flame or electric discharge, but only in packets that contain the exact amount of energy necessary to allow the electron to move farther from the uucleus into a higher energy level/energy state. When this happens, we say that the atom is in an excited state. When the electron returns to a lower energy level, it emits the previously absorbed energy in the form of packets of light called photons. These photons/packets of light ave a specific wavelength and energy equal to the difference between the two energy levels. Why does the light emitted from an excited neon atom look red to the human eye and iulticolored when viewed through a prism or spectroscope? In a given atom, many xcited states are possible due to the existence of a number of energy levels. When light is nitted by excited atoms, a variety of energies of light are released as the electrons return to eir lowest energy level. The naked eye perceives the sum of these emissions as colored light, $$ y $$ red or blue. For example, the color of fireworks is the sum of the various excitations of ectrons in metallic salts. When this emitted light is passed through a prism or a diffraction grating in a spectroscope ne spectrum is seen. Each line in the line spectrum corresponds to a packet of light of a ticular energy. This packet of light is emitted by the excited atom when electrons fall to low rgy levels from the excited state. Each element has its own unique line spectrum due to erences in the possible energy level transitions in atoms of different elements. The analys ne light emitted from atoms is used to determine the identity of elements in water, the sta many other types of matter.

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To determine which wave, $$ A $$ or $$ B $$, is of higher energy, we need to understand the relationship between the energy of a wave and its frequency or wavelength. The energy $$ E $$ of a photon (light wave) is given by the equation:

$$
E = h \cdot f
$$

where:
- $$ E $$ is the energy of the photon,
- $$ h $$ is Planck's constant ($$6.626 \times 10^{-34} \, \text{Js}$$),
- $$ f $$ is the frequency of the wave.

Alternatively, since frequency and wavelength ($$ \lambda $$) are related by the speed of light ($$ c $$), we can express energy in terms of wavelength:

$$
E = \frac{h \cdot c}{\lambda}
$$

where:
- $$ c $$ is the speed of light ($$3.00 \times 10^8 \, \text{m/s}$$).

From these equations, we can conclude:
- Higher frequency waves have higher energy.
- Shorter wavelength waves have higher energy.

### Step-by-Step Analysis

1. **Identify the Wavelengths**: If the diagram provides the wavelengths of waves $$ A $$ and $$ B $$, we can directly compare them. If $$ A $$ has a shorter wavelength than $$ B $$, then $$ A $$ has higher energy.

2. **Identify the Frequencies**: If the frequencies of waves $$ A $$ and $$ B $$ are provided, we can compare them directly. The wave with the higher frequency has higher energy.

3. **Conclusion**: Based on the information from the diagram, we can determine which wave has higher energy.

### Explanation of Light Emission from Atoms

Atoms produce visible light through the excitation and relaxation of electrons. Here’s a breakdown of the process:

1. **Excitation**: When an atom absorbs energy (from heat, light, or electricity), its electrons can move to higher energy levels. This state is called the excited state.

2. **Emission of Photons**: When the excited electrons return to their original (lower) energy levels, they release energy in the form of photons. The energy of these photons corresponds to the difference in energy between the two levels.

3. **Color of Light**: The color of the emitted light depends on the energy of the photons. Different transitions between energy levels result in different wavelengths of light, which correspond to different colors. For example, neon emits red light due to specific transitions in its energy levels.

4. **Spectroscopy**: When the emitted light passes through a prism or diffraction grating, it separates into a spectrum. Each line in the spectrum represents a specific energy transition, allowing us to identify the element based on its unique spectral lines.

### Summary

- To determine which wave has higher energy, compare their wavelengths or frequencies.
- Atoms emit visible light when electrons transition between energy levels, with the emitted light's color depending on the energy difference of these transitions. Each element has a unique emission spectrum, which can be analyzed to identify the element.
Wave $$ A $$ has higher energy than wave $$ B $$ because it has a shorter wavelength. Atoms produce visible light when electrons move between energy levels. The color of the light depends on the energy difference between these levels. Each element has a unique light emission pattern, which helps identify it.

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