Question

An electron made a transition between allowed states emitting a photon. What physical constants are needed to calculate the energy of photon from the measured wavelength? (select all that apply) a) the Plank constant, \(h\) b) the basic electric charge, \(e\) c) the speed of light in vacuum, \(c\) d) the Stefan-Boltzmann constant, \(\sigma\)

Short answer

Answer: a) the Planck constant (h), c) the speed of light in vacuum (c)

Step-by-step solution

1. Identify the energy-wavelength relationship for a photon

The energy of a photon (E) can be found using the following equation: E = h * c / λ, where: - E is the energy of the photon, - h is the Planck constant, - c is the speed of light in vacuum, and - λ is the wavelength of the photon.

2. Analyze the equation for required constants

From the energy-wavelength relationship, we can see that only two physical constants are involved in the calculation: - The Planck constant (h) - The speed of light in vacuum (c)

3. Conclusion

The physical constants needed to calculate the energy of the photon from the measured wavelength are: a) the Planck constant, \(h\) c) the speed of light in vacuum, \(c\) The other given constants, the basic electric charge (e) and the Stefan-Boltzmann constant (σ), are not required for this calculation.

Key concepts

Planck Constant

The Planck constant, denoted by the symbol \(h\), is a fundamental constant in physics that plays a crucial role in quantum mechanics. It relates the energy of a photon to the frequency of its associated electromagnetic wave. The value of the Planck constant is approximately \(6.626 \times 10^{-34}\) joule-seconds (J·s).Understanding the Planck constant helps in comprehending how energy is quantized in small, discrete packets called quanta. This concept introduced the groundbreaking idea that energy is not continuous, as previously believed, but instead exists in these tiny, indivisible units. This realization was fundamental to the development of quantum theory.In practical terms, when calculating photon energy, \(h\) serves as a bridge connecting the photon’s frequency (or equivalently, its wavelength) to its energy. This concept is pivotal when exploring interactions at the atomic and subatomic levels.

Speed of Light

The speed of light in a vacuum is a critical constant in physics, denoted by \(c\). It measures about \(3 \times 10^8\) meters per second. This speed is not just a property of light but a fundamental aspect of the universe, influencing everything from the propagation of electromagnetic waves to the interaction of particles.As a major component in calculations involving electromagnetic radiation, the speed of light helps determine the energy of photons. It appears in the formula for photon energy as \(E = \frac{hc}{\lambda}\), tying together the concepts of energy, frequency, and wavelength.When thinking about the speed of light, it's essential to recognize that it sets the ultimate speed limit for how quickly information and matter can travel. Its constancy is a cornerstone of Einstein's theory of relativity and impacts how we understand space and time.

Wavelength-Energy Relationship

The relationship between a photon's wavelength and its energy is a fundamental concept in understanding how electromagnetic radiation behaves. As laid out in the equation \(E = \frac{hc}{\lambda}\), energy \(E\) is inversely proportional to the wavelength \(\lambda\), implying that shorter wavelengths correspond to higher energies.This relationship means that different types of electromagnetic waves, which vary in wavelength, carry different amounts of energy. For example:

• X-rays have very short wavelengths and thus, high energy, making them capable of penetrating substances like skin and tissue.
• Radio waves, which have much longer wavelengths, carry much less energy and are used for communication over long distances without significant absorption by materials in between.

Grasping the wavelength-energy relationship allows us to better understand phenomena like how certain materials absorb light, why ultraviolet rays are more damaging to the skin than visible light, and how solar panels convert sunlight into electricity.