SELECTED PROBLEMS OF MODERN PHYSICS I. THE PHOTOELECTRIC EFFECT

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SELECTED PROBLEMS OF MODERN PHYSICS

I. THE PHOTOELECTRIC EFFECT

  1. How to demonstrate experimentally that photoelectrons are emitted from an illuminated metallic surface?        

Ultraviolet light cause emission of free negative charges (photoelectrons)  from metal surfaces. We can show this phenomena in a simple experiment. A freshly polished plate of zinc connected with an electroscope is charged negatively. When the plate is illuminated by visible light only, nothing happens (the charge on its surface is constant). But when we illuminate the plate using ultraviolet light, a discharge is observed  the leafs of the electroscope slowly fall. This is a result of electron emission from the zinc plate.

What is important, we see that in case of zinc, the photoelectric effect takes place only when we replace the visible light with ultraviolet, which has a higher light-wave frequency.

  1. Explain how the magnitude of photocurrent depends on light intensity.

The magnitude of this photocurrent increases in proportion to light intensity.(fig.5.2)

But increasing the intensity of light increases the number of photoelectrons, NOT their velocity (so increasing magnitude means growing number of photoelectrons)

  1. Explain the dependence between photocurrent and the potential difference existing between a cathode and an anode.

When the positive potential difference increases, the photocurrent reaches a point of saturation, due to limited number of photocurrent ejected from the cathode at a given light intensity  the bigger light intensity I is, the  bigger is the value of point of saturation  question no 2. When the potential difference approaches 0, the photocurrent  decrease. (Fig.5.3)

 

  1. What is a stopping potential?

It is certain negative potential of the anode necessary to cause a photocurrent decay. It is create by changing the polarity of voltage. It is the only way to stop the photoelectrons.

The low positive potential of the anode is conductive to the formation of a cloud of photoelectrons at the cathode, which inhibits the movement of photoelectrons towards the anode but DON’T STOP THEM. Even when the potential difference equal zero, a number of photoelectrons are ejected from the cathode with a velocity high enough to overcome the negative space charged and reach the anode.

 

The stopping potential does not depends on light intensity (so the maximum velocity of photoelectrons does not depend on light intensity)

  1. What is a threshold frequency of a photocurrent, ν0?

It is a photocurrent-frequency below which no electrons are emitted from the cathode’s surface. Its magnitude depends on the material of the cathode.  (Fig.5.5)

If frequency of light is less than ν0, the photoelectric effect does not occur even if light intensity I is very high. But when we use light with ν> ν0 electrons are ejected almost immediately even in dim light.

In low-frequency light, photons have less energy than the work function. These photons are unable to eject electrons even when light intensity is high. The threshold frequency follows from the photoelectric equation, for the condition  Wmax=0

0 = Φ

question no 6

For most of the metals, the threshold frequency lies in the ultraviolet, where frequency is relatively high. For alkaline metals, ν0 lies in the visible and near-infrared spectrum.

  1. How does Einstein explain the photoelectric effect?

Following the earlier idea of Planck’s, Einstein proposed that light consists of ”light quanta” (often called protons), that have energy E = hν, where h is the Planck’s constant and which behave like material particle. A light quantum which collides with a metal surface is completely absorbed and imparts its total energy to a single electron. Part of this energy, W0, is consumed to pull a surface electron out of the metal; this is called the work function, Φ.

If the energy of a photon is more than Φ, then the energy remaining after absorbing the photon is used for giving the electron a kinetic energy, W=1/2mv2.  

According to the law of conservation of energy, Einstein proposed his photoelectric equation:

hν = Φ + Wmax

This energy would have a maximum value of Wmax=1/2mv2max if an ejecting electron belonged to the outer atomic layer. If a photon is absorbed by an electron which lies deeper, more energy than Φ is necessary to pull it out.

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  1. How to determine the work function?

Work function, Φ, is the part of energy given to a single electron by a light quantum which collides with a metal surface. This energy is needed to pull a surface electron out of the material. The work function depends on the particular metal (table5.1)  

  1. Find the relation between stopping potential and light frequency.

Stopping potential is the negative potential of the anode needed to stop photoelectrons. When it is reached even the fastest photoelectrons are not able to reach it, which means that ν0 can be expressed ...

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