3.)tunnel and photoelectric effects

In summary, tunneling is possible when the energy of the particle is less than the barrier's work function and the particle is in an excited state for a short amount of time.
  • #1
GAGS
55
0
hello,
'QUERY3
I think we all know about tunnel effect of quantum, Also when I was studying photoelectric effect, I studied that emission of electrons for a electro-magnteic radiation of frequency less than threshold frequency is quite impossible.
But then how can we say that particle having less energy than that of barrier,is probable to pass through or in short having finite TRANSMISSION PROBABILITY
 
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  • #2
Tunneling has three components: 1) energy of the particle, 2) energy of the barrier, and 3) width of the barrier. Obviously, we would decrease tunneling with an increased barrier width.

Well, the case of the photoelectric effect, the energy barrier is the difference in the vacuum level and the Fermi level; this is called the workfunction of the metal. How about the width of the barrier? Well if we're just talking about metal to vacuum, then the barrier width is infinite. Therefore tunneling will not occur.
 
  • #3
GAGS said:
hello,
'QUERY3
I think we all know about tunnel effect of quantum, Also when I was studying photoelectric effect, I studied that emission of electrons for a electro-magnteic radiation of frequency less than threshold frequency is quite impossible.
But then how can we say that particle having less energy than that of barrier,is probable to pass through or in short having finite TRANSMISSION PROBABILITY

In addition to what has been said, there is also another aspect that you need to consider - the length of time that the electron is in a particular state.

When an electron is in the ground state of the conduction band (i.e. the top of the Fermi level), the "barrier", which is the work function, is rather large. This means that the probability of transmission is very, very small to insignificant. Now, if you excite it with a photon of energy less than the work function, the electron will be in an excited state that sees a potential barrier that is less than the work function. So technically one expects some transmission probability. However, the particle isn't in that excited state for very long. For a metal, the lifetime of the electron to be in that state is of the order of femtoseconds. It doesn't get to see that kind of potential barrier that long before it decays back to the ground state. So even though it did see a smaller potential barrier that might allow it to have a significant transmission probability, the shortness of the lifetime will be a major factor on the lack of any detected transmission.

Note that there are ways to change the nature of the potential barrier and still allow for a longer "lifetime" to enable a transmission. Field emission phenomenon does exactly just that. By applying a strong electric field on the surface of the metal, one can actually reduce the width of the potential barrier for the electrons at the Fermi level. At a sufficiently high enough electric field, you can start to observe significant tunneling effect from electrons at the Fermi level going through the barrier and leaving the metal. This is what is described in the Fowler-Nordheim model for field emission.

Zz.
 
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1. What is tunnel effect?

Tunnel effect is a quantum mechanical phenomenon in which a particle has the ability to penetrate through a potential barrier even though it does not have enough energy to overcome it. This effect is possible due to the wave-like nature of particles at the quantum level.

2. What is photoelectric effect?

Photoelectric effect is the phenomenon in which electrons are emitted from a material when it is exposed to light. This effect occurs due to the interaction between photons (light particles) and electrons in the material, which causes the electrons to gain enough energy to overcome the binding forces holding them in the material and escape as free electrons.

3. What is the significance of tunnel and photoelectric effects?

Tunnel and photoelectric effects have significant implications in the field of quantum mechanics and have led to the development of many modern technologies such as transistors, solar cells, and photodetectors. They also provide valuable insights into the dual nature of particles as both waves and particles.

4. How are tunnel and photoelectric effects related?

Both tunnel and photoelectric effects involve the transfer of energy between particles. In tunnel effect, a particle gains energy to overcome a potential barrier, while in photoelectric effect, energy is transferred from photons to electrons. Additionally, both effects are governed by the principles of quantum mechanics.

5. Can tunnel and photoelectric effects occur simultaneously?

Yes, it is possible for both tunnel and photoelectric effects to occur simultaneously. For example, in a photovoltaic cell, photons can transfer energy to electrons, causing the photoelectric effect, while the electrons can also tunnel through potential barriers to produce electric current. This phenomenon is known as the tunneling photoelectric effect.

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