To answer the question about the equation used by Albert Einstein to explain the photoelectric effect, let us delve into the principles of the photoelectric effect itself.
Einstein discovered that when light (or more generally, electromagnetic radiation) of a certain frequency shines on a metal surface, it can cause the surface to emit electrons. This phenomenon cannot be explained by classical wave theory alone and led Einstein to propose his groundbreaking idea using quantum theory.
The key relation he introduced is based on the concept of energy quantization. According to Einstein, the energy ([tex]\(E\)[/tex]) of a photon of light is directly proportional to the frequency ([tex]\(v\)[/tex]) of the light, and the constant of proportionality is Planck's constant ([tex]\(h\)[/tex]).
The correct equation that describes this relationship is:
[tex]\[ E = h \cdot v \][/tex]
Here's a brief explanation of each term:
- [tex]\( E \)[/tex] is the energy of the photon.
- [tex]\( h \)[/tex] is Planck's constant, which is a fundamental constant in quantum mechanics.
- [tex]\( v \)[/tex] is the frequency of the electromagnetic radiation.
Let's review the provided options in the question:
1. [tex]\( E = \frac{h}{v} \)[/tex] – This states that the energy is inversely proportional to the frequency, which is incorrect.
2. [tex]\( E = h \cdot v \)[/tex] – This correctly states that the energy is directly proportional to the frequency, matching Einstein's description.
3. [tex]\( E = \frac{\nu}{h} \)[/tex] – This incorrectly states that the energy is directly proportional to the frequency divided by Planck's constant, which is not correct in this context.
4. [tex]\( E = h - v \)[/tex] – This falsely adds Planck's constant and frequency, which does not align with the physical theory.
Thus, the correct equation used by Albert Einstein to explain the photoelectric effect is:
[tex]\[ E = h \cdot v \][/tex]
And the correct option from the given choices is:
[tex]\[ \text{Option 2: } E = h \cdot v \][/tex]
