Maximum kinetic energy electrons emitted from the metal under the action of light is 1.2 eV. If we reduce the wavelength of the incident light by a factor of 2, then the maximum kinetic energy of electrons emitted from the same metal becomes 3.95 eV. Determine the energy of the incident photons in the first case.

Answer:

Photoelectric effect equation: Here, the left side is the energy of the incident photon. h \u003d 4.136 * 10 ^ (-15) eV * s v - Greek letter nu, photon frequency. c = 3*10^8 m/s is the speed of light in vacuum. The wavelength of a photon is denoted by the Greek letter lambda l Hence h*v = h*c/l Right side. A is the work function, it does not change. mv^2/2 is the max. kinetic energy of emitted electrons. We have mv^2/2 = 1.2 eV. If the wavelength is reduced by 2 times, then on the left it will be 2h * c / l, and on the right mv ^ 2/2 = 3.95 eV. We get the system ( h * c / l \u003d A + 1.2 ( 2h * c / l \u003d A + 3.95 Subtract from equation 2 1 the equation h * c / l \u003d 3.95 - 1.2 \u003d 2.75 eV Answer: 2.75 eV

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Briefly

photoelectric effect is the emission of electrons by a substance under the action of light (and, generally speaking, any electromagnetic radiation). In condensed substances (solid and liquid), external and internal photoelectric effects are distinguished.

Laws of the photoelectric effect:

1st law of photoelectric effect: the number of electrons ejected by light from the surface of a metal per unit time at a given frequency is directly proportional to the light flux illuminating the metal.

2nd law of photoelectric effect: the maximum kinetic energy of electrons ejected by light increases linearly with the frequency of light and does not depend on its intensity.

3rd law of photoelectric effect: for each substance there is a red border of the photoelectric effect, that is, the minimum frequency of light ν 0 (or maximum wavelength λ 0 ), at which the photoelectric effect is still possible, and if ν < ν 0 , then the photoelectric effect no longer occurs.

Electromagnetic radiation is a stream of individual quanta (photons) with energy hν each, where h is Planck's constant. With the photoelectric effect, part of the incident electromagnetic radiation is reflected from the metal surface, and part penetrates into the surface layer of the metal and is absorbed there. Having absorbed a photon, the electron receives energy from it and, doing the work function, leaves the metal: hν = A out + W e, where W e is the maximum kinetic energy that an electron can have when it leaves the metal.

From the law of conservation of energy, when light is represented in the form of particles (photons), Einstein's formula for the photoelectric effect follows:

hν = A out + E k

A out is the work function (the minimum energy required to remove an electron from a substance),

E k is the kinetic energy of the emitted electron (depending on the velocity, it can be calculated as the kinetic energy relativistic particle, and no),

ν is the frequency of the incident photon with energy hν,

h is Planck's constant.

in detail

The photoelectric effect is the phenomenon of ejection of electrons from solid and liquid bodies under the influence of light.

Discovered the photoelectric effect Heinrich Hertz(1857 - 1894) in 1887 year. He noticed that the jumping of a spark between the balls of the spark gap is greatly facilitated if one of the balls is illuminated with ultraviolet rays.

Then in 1888-1890 1990s, he studied the photoelectric effect Alexander Grigorievich Stoletov(1839 – 1896).

He established that:

  • ultraviolet rays have the greatest effect;
  • with an increase in the luminous flux, the photocurrent increases;
  • the charge of particles emitted from solid and liquid bodies under the action of light is negative.

In parallel with Stoletov, the photoelectric effect was studied by a German scientist Philip Lenard(1862 – 1947).

They established the basic laws of the photoelectric effect.

Before formulating these laws, let us consider a modern scheme for observing and studying the photoelectric effect. She is simple. Two electrodes (cathode and anode) are soldered into the glass cylinder, to which voltage U is applied. In the absence of light, the ammeter indicates that there is no current in the circuit.

When the cathode is illuminated with light, even in the absence of voltage between the cathode and the anode, the ammeter shows the presence of a small current in the circuit - photocurrent. That is, the electrons that have flown out of the cathode have some kinetic energy and reach the anode “on their own”.

As the voltage increases, the photocurrent increases.

The dependence of the photocurrent on the voltage between the cathode and the anode is called the current-voltage characteristic.

It has the following form. At the same intensity monochromatic light as the voltage increases, the current first increases, but then its growth stops. Starting from a certain value of the accelerating voltage, the photocurrent ceases to change, reaching its maximum (at a given light intensity) value. This photocurrent is called the saturation current.

To "lock" the photocell, that is, reduce the photocurrent to zero, it is necessary to apply a "blocking voltage". In this case, the electrostatic field does work and slows down the emitted photoelectrons

This means that none of the electrons emitted from the metal reaches the anode if the anode potential is lower than the cathode potential by a value.

The experiment showed that when the frequency of the incident light changes, the starting point of the graph shifts along the stress axis. It follows from this that the magnitude of the blocking voltage, and, consequently, the kinetic energy and maximum velocity of the emitted electrons, depend on the frequency of the incident light.

The first law of the photoelectric effect. The value of the maximum velocity of the emitted electrons depends on the frequency of the incident radiation (increases with increasing frequency) and does not depend on its intensity.

If we compare the current-voltage characteristics obtained at different intensities (in Figures I 1 and I 2) of incident monochromatic (single-frequency) light, we can notice the following.

First, all current-voltage characteristics originate at the same point, that is, at any light intensity, the photocurrent vanishes at a specific (for each frequency value) retarding voltage. This is another confirmation of the fidelity of the first law of the photoelectric effect.

Secondly. With an increase in the intensity of the incident light, the nature of the dependence of the current on the voltage does not change, only the magnitude of the saturation current increases.

The second law of the photoelectric effect. The value of the saturation current is proportional to the value of the luminous flux.

When studying the photoelectric effect, it was found that not all radiation causes a photoelectric effect.

The third law of the photoelectric effect. For each substance there is a minimum frequency (maximum wavelength) at which the photoelectric effect is still possible.

This wavelength is called the "red border of the photoelectric effect" (and the frequency - corresponding to the red border of the photoelectric effect).

5 years after the appearance of the work of Max Planck, Albert Einstein used the idea of ​​the discreteness of light emission to explain the patterns of the photoelectric effect. Einstein suggested that light is not only emitted in batches, but also propagated and absorbed in batches. This means that the discreteness of electromagnetic waves is a property of the radiation itself, and not the result of the interaction of radiation with matter. According to Einstein, a radiation quantum resembles a particle in many ways. A quantum is either completely absorbed or not absorbed at all. Einstein imagined the escape of a photoelectron as the result of a collision of a photon with an electron in a metal, in which all the energy of the photon is transferred to the electron. So Einstein created quantum theory light and, based on it, wrote an equation for the photoelectric effect:

This equation explained everything experimentally established laws photoelectric effect.

  1. Since the work function of an electron from a substance is constant, then, with increasing frequency, the speed of electrons also increases.
  2. Each photon knocks out one electron. Therefore, the number of ejected electrons cannot be more number photons. When all the ejected electrons reach the anode, the photocurrent stops growing. As the light intensity increases, so does the number of photons incident on the surface of matter. Consequently, the number of electrons that these photons knock out increases. In this case, the saturation photocurrent increases.
  3. If the energy of photons is only enough to perform the work function, then the speed of the emitted electrons will be equal to zero. This is the "red border" of the photoelectric effect.

The internal photoelectric effect is observed in crystalline semiconductors and dielectrics. It consists in the fact that under the influence of irradiation, the electrical conductivity of these substances increases due to an increase in the number of free current carriers (electrons and holes) in them.



This phenomenon is sometimes called photoconductivity.

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