Question

The energy of a photon of visible light emitted by an excited atom is the energy change that takes place within the atom itself.

Short answer

When an excited electron in an atom drops to a lower energy level, the energy difference between the two levels is released as a photon. The energy of the emitted photon (\(E_\text{photon}\)) is equal to the change in energy within the atom (\(\Delta E_\text{atom}\)). This relationship can be expressed using the formula \[ \Delta E_\text{atom} = \frac{hc}{\lambda} \], where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the photon.

Step-by-step solution

Understand the concept of an excited atom

An atom becomes excited when it absorbs energy, usually in the form of electromagnetic radiation. This causes one or more of its electrons to move to a higher energy level. When one of these excited electrons returns to a lower energy level, it releases energy in the form of a photon - a particle that carries electromagnetic radiation like visible light.

Understand electron energy levels in an atom

Electrons in an atom can occupy specific energy levels. These energy levels can be depicted as concentric circles around an atom's nucleus, with each circle representing a higher energy level. When an electron moves from one energy level to another, an energy change occurs.

Learn about the formula for the energy of a photon

The energy of a photon (E) is calculated using the following formula: \[ E = h \cdot f \] where \(h\) represents Planck's constant (\(6.63 \times 10^{-34} \, J \cdot s\)), and \(f\) is the frequency in Hz of the photon. We can also write this equation in terms of the photon's wavelength, using the relationship between frequency and wavelength: \[f = \frac{c}{\lambda}\] where \(c\) represents the speed of light (\(3.00 \times 10^{8} \, m/s\)), and \(\lambda\) is the wavelength of the photon in meters. Substituting this into the equation for the energy of a photon yields: \[ E = \frac{hc}{\lambda} \]

Understand the relationship between photon energy and energy change in an atom

When an electron in an excited atom drops to a lower energy level, the difference in energy between the two levels is released as a photon. Therefore, the energy of the emitted photon is equal to the change in energy within the atom: \[ E_\text{photon} = \Delta E_\text{atom} \] To find the energy change within the atom, we can use the formula for photon energy: \[ E_\text{photon} = \frac{hc}{\lambda} \] And replace \(E_\text{photon}\) with \(\Delta E_\text{atom}\): \[ \Delta E_\text{atom} = \frac{hc}{\lambda} \]

Use the modified formula to calculate the energy change in the atom

Now that we have the formula relating photon energy to the energy change within an atom, we can use it to calculate the energy change when a photon of visible light is emitted: \[ \Delta E_\text{atom} = \frac{hc}{\lambda} \] In this equation, \(h\) and \(c\) are constants, so we only need to know the wavelength of the photon to determine the energy change within the atom.

Key concepts

Excited Atom

Atoms become excited when they absorb external energy. This energy can come from sources like electromagnetic radiation, which stimulates the atom’s electrons. When electrons absorb this energy, they move to higher energy levels within the atom.
This state of having electrons in a higher energy level is what we call an "excited atom."
However, this excited state is not stable.

Electrons in higher energy levels will eventually return to a lower level. During this transition, the electron releases energy in the form of a photon. This photon carries visible light or other forms of electromagnetic radiation.
The emitted light gives insight into the energy changes that occur within an atom. This process is crucial in understanding how atoms interact with light.

Electron Energy Levels

An atom consists of electrons that orbit its nucleus in specific paths, known as energy levels or shells.
These energy levels can be visualized as concentric circles around the nucleus of the atom.
The electrons in each of these levels have a set amount of energy.

When an electron jumps from a lower level to a higher level, it must absorb energy. This absorption often reflects in the behavior of the electrons as they move between these levels.

• Lower energy levels are closer to the nucleus and are more stable.
• Higher energy levels are further from the nucleus and require electrons to have more energy.

When an electron descends to a lower level, it releases energy equal to the difference between the levels.
This released energy manifests as a photon (

Planck's Constant

Planck's constant is a fundamental figure in the world of quantum mechanics. It denotes the relationship between the energy of a photon and its frequency. Denoted by the symbol \( h \), Planck's constant has a value of \( 6.63 \times 10^{-34} \, J \cdot s \).
This constant is crucial when calculating photon energy using the following formula:

\[ E = h \cdot f \]

Where \( E \) is the energy of the photon, and \( f \) is its frequency.
This formula helps us understand the quantized nature of energy in the realm of photons.

We can also express the energy in terms of wavelength by using the equation:

\[ E = \frac{hc}{\lambda} \]

In this equation, \( c \) is the speed of light, and \( \lambda \) is the wavelength.

• Planck's constant acts as a bridge between the physical world of particles and the wave nature of light.
• It showcases how energy transitions between quantized states.

Planck's constant highlights the discrete nature of atomic and subatomic systems.