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The frequency of a wave tells us how often the wave's crest passes a certain point in one second. It's measured in hertz (Hz), which means cycles per second. For photons and other electromagnetic waves, frequency is a fundamental property because it relates directly to energy.

In our problem, the frequency of the photon is given as \(5.6 \times 10^{14}\) Hz. This high frequency suggests that the photon belongs to the visible or near-infrared part of the electromagnetic spectrum, which is common in many atomic transitions.

It’s important to recognize that frequency has a direct relationship with energy. Higher frequency means higher energy. This is described quantitatively by the formula \(E = h \cdot f\), where \(E\) is energy, \(f\) is frequency, and \(h\) is Planck's constant. Understanding this relationship is key in fields such as quantum physics and chemistry, where energy levels and transitions are critical.

• Frequency helps determine the energy of a photon.
• More frequent waves, i.e., higher frequency, carry more energy.
• Frequency is tied closely with color and energy in atomic processes.

Planck’s constant is a fundamental constant in quantum mechanics, symbolized as \(h\). Its value is approximately \(6.626 \times 10^{-34}\) joule-seconds (Js). This seemingly small number plays a huge role in the realm of particles and waves.

When Max Planck introduced this constant, it was to solve the ultraviolet catastrophe in black-body radiation. However, it opened the door to quantum theory, revolutionizing physics by suggesting that energy is quantized, or comes in packets, called quanta or photons for light.

Planck's constant links the frequency of a photon to its energy through the relationship \(E = h \cdot f\). This formula shows that even small changes in frequency produce significant changes in energy, illustrating why Planck’s constant is so pivotal in describing the behavior of subatomic particles.

• Symbolized by \(h\) and valued at \(6.626 \times 10^{-34}\) Js.
• Essential for calculating photon energies.
• Foundation of quantum mechanics, connecting wave and particle duality.

Atomic absorption occurs when an atom takes in energy from a photon, resulting in a change in the atom’s energy level. When a photon is absorbed, its energy is transferred to the atom, often exciting an electron to a higher energy state or level.

In the context of our exercise, the atom absorbs a photon with a frequency of \(5.6 \times 10^{14}\) Hz. This absorption causes the energy of the atom to increase by \(3.7116 \times 10^{-19}\) J, exactly the energy of the photon that was absorbed. This is a perfect example of how the conservation of energy principle works at an atomic level.

Understanding atomic absorption is crucial in spectroscopy and quantum chemistry, where researchers investigate how substances interact with different light frequencies.

• Photon absorption leads to an increase in atomic energy.
• Energy gain corresponds to the energy of the absorbed photon.
• Key concept in fields like spectroscopy and chemical analysis.