Every person who is familiar with physics knows that electrical energy can be obtained in various ways. These include the phenomenon of electromagnetic induction, the Seebeck effect and the photoelectric effect. The last of them will be discussed in this article. In parallel, we consider the question of what is the red border of the photoelectric effect.
What is a photo effect?
Answering briefly to this question, it should be said that this is a phenomenon in which photons incident on a material “pull out” electrons from it. This phenomenon is called an external photoelectric effect. It was discovered by Hertz in 1887, and Einstein gave an explanation to it in 1905.
Einstein examined the light interacting with matter in the form of a beam of quanta. Each quantum is absorbed by the electron of the atom and transfers all its energy to it. If the energy exceeds the set threshold value, then the electron breaks away from the atomic nucleus and becomes free.
Note that Einstein’s idea of the quantum nature of the interaction of light with material was shocking for physics at the beginning of the 20th century, since at that time many experiments and theoretical calculations had already confirmed that light is an electromagnetic wave.
Einstein's equation and the red border of the photoelectric effect
In 1905, publishing his theory of the processes occurring during the photoelectric effect, Einstein gave an important formula, which now bears his last name. It is written in the following form:
h * v = A + E k
This formula is simple to understand: a quantum of electromagnetic radiation with an energy of h * v, where h = 4.13567 * 10 -15 is the Planck constant in eV * s, v is the frequency of the wave in hertz, expends its energy to perform work A against electrostatic forces and kinetic energy (E k ) to the electron.
Einstein's formula shows that if h * v <A, then the photoelectric effect does not occur. This fact is confirmed experimentally. One of the laws of the photoelectric effect says that the kinetic energy of the “ripped out” electron does not depend on the radiation intensity, but is in direct proportion to the frequency v.
If E k = 0, then h * v = h * v 0 = A. The frequency v 0 , which corresponds to the photon energy value equal to the work A, is called the red border. Accordingly, the wavelength of the red border of the photoelectric effect is calculated by the formula:
λ 0 = c / v 0
Here c is the speed of light. The wavelength λ 0 is the largest at which the photoelectric effect is manifested. For any lengths λ> λ 0, the photons will only transfer the electron to the excited state, but they will not be able to “tear it” away from the nucleus.
The red border of the photoelectric effect is called by analogy with the visible emission spectrum, in which red has the longest wavelength.
Problem solving example
We will solve the following problem: it is necessary to answer the question whether the photoelectric effect will be observed if gold is irradiated with a monochromatic light beam with a wavelength of 300 nm.
First, find the red border of the photoelectric effect for gold. Turning to the tabular data, we write out the electron work function for gold. It is 5.1 eV. The red border for the metal is calculated by the formula:
λ 0 = c / v 0 = c * h / A
Substitute the values, we get:
λ 0 = 3 * 10 8 * 4.13567 * 10 -15 / 5.1 = 2.43 * 10 -7 m or 243 nm
Since the wavelength of light that will be irradiated by gold (300 nm) is greater than the value of the red border for it (243 nm), the photon energy will not be enough to "pull" the electrons from the atom of this metal, that is, there will be no photoelectric effect.