Let’s break down your questions step by step, starting with the equation E=pc and its validity for photons. This equation is derived from the principles of special relativity and quantum mechanics, specifically for massless particles like photons.
Understanding E=pc for Photons
The equation E=pc indicates that the energy (E) of a photon is directly proportional to its momentum (p). Here’s how we arrive at this conclusion:
- De Broglie Wavelength: The de Broglie equation states that the wavelength (λ) of a particle is given by λ = h/p, where h is Planck's constant and p is momentum. For photons, which are massless, this relationship holds true.
- Energy-Wavelength Relationship: The energy of a photon can also be expressed as E = hc/λ, where c is the speed of light. Substituting λ from the de Broglie equation into this energy equation gives us E = pc.
Since photons have no rest mass, they travel at the speed of light, and thus the relationship E=pc is specifically valid for them. For particles with mass, the full energy-momentum relation is E² = (pc)² + (m₀c²)², which incorporates rest mass (m₀).
Examining KE(max) = eV₀
Now, let’s discuss the equation KE(max) = eV₀. This equation is true and relates to the maximum kinetic energy of an electron ejected from a material when it absorbs energy from a photon, such as in the photoelectric effect.
- Photoelectric Effect: When light shines on a metal surface, photons can transfer their energy to electrons. If the energy of the photon (E = hν) exceeds the work function (Φ) of the metal, the excess energy is converted into kinetic energy of the ejected electron.
- Energy Transfer: The maximum kinetic energy of the ejected electron is given by KE(max) = E - Φ. If we define the photon energy as eV₀ (where V₀ is the stopping potential), then KE(max) = eV₀ holds true.
True or False Statements about Photons
Now, let’s evaluate the statements regarding two photons:
a) Equal E have equal P (momentum)
This statement is True. Since momentum p is given by p = E/c for photons, if two photons have equal energy, they must also have equal momentum, as they both travel at the speed of light.
b) Equal p have equal λ
This statement is True. From the de Broglie relation, λ = h/p, if two photons have equal momentum, they will have equal wavelengths, as wavelength is inversely proportional to momentum.
c) Equal λ have equal p (momentum)
This statement is True. Again, using the de Broglie relation, if two photons have equal wavelengths, they must have equal momentum, since momentum is inversely related to wavelength.
In summary, the relationships between energy, momentum, and wavelength for photons are tightly interwoven through fundamental principles of physics. Each statement regarding the properties of photons holds true based on these principles, illustrating the elegant consistency of quantum mechanics and relativity.
