Minimum wavelength of electrons ejected from metal

In summary, the problem has two parts. Part a involves calculating the wavelength of photons produced by a laser with energy E = 3.5eV, assuming an index of refraction of 1.6. The answer is 221nm. Part b involves finding the minimum wavelength of electrons ejected from a metal with a work function of φ=1.5eV in vacuum when a laser beam is focused on its clean surface. The answer is 0.867nm. The equations used are E = hv/λ and KEmax = hf - φ.
  • #1
auleiia
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Homework Statement



This problem has two parts.

A laser produces photons having an energy, E = 3.5eV.
a) What is the wavelength of photons produced, assuming that the index of refraction is 1.6? ->221nm
b) If this laser beam is focused on the clean surface of a metal having a work function of φ=1.5eV in vacuum, what is the minimum wavelength λmin of the electrons that will be ejected from the metal? Assume that the experiment is done in a vacuum. -> .867nm

Homework Equations



E = hv/λ
KEmax = hf - φ

The Attempt at a Solution


So I understand part a. It's simply λ = hv/E, where v is calculated using index of refraction. However I am stuck on part B, where the answer is .867 nm. At first I was trying to do λ = hc/φ, since v = c since it is in a vacuum, and since the minimum frequency will be when KE = 0 then hf = φ, however that gives me 826nm which is not correct, or even close to being correct.
 
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  • #2
The question is asking for the minimum wavelength of the ejected electrons (de Broglie wavelength).
 

FAQ: Minimum wavelength of electrons ejected from metal

1. What is the minimum wavelength of electrons ejected from metal?

The minimum wavelength of electrons ejected from metal is determined by the work function of the metal, which is the minimum amount of energy required to eject an electron. This value varies depending on the type of metal and can range from a few electronvolts to several electronvolts.

2. How does the minimum wavelength of electrons ejected from metal relate to the photoelectric effect?

The minimum wavelength of electrons ejected from metal is directly related to the photoelectric effect. The photoelectric effect is the phenomenon where electrons are emitted from a metal surface when it is exposed to light of a certain frequency. The minimum wavelength of electrons is determined by the frequency of the incident light, which must be equal to or greater than the work function of the metal for electrons to be ejected.

3. Can the minimum wavelength of electrons ejected from metal be measured?

Yes, the minimum wavelength of electrons ejected from metal can be measured using various techniques such as photoelectron spectroscopy. This involves shining light of different frequencies on the metal surface and measuring the kinetic energy of the emitted electrons. The minimum wavelength can then be calculated using the equation E = hf, where E is the kinetic energy of the electron, h is Planck's constant, and f is the frequency of the incident light.

4. How does the minimum wavelength of electrons ejected from metal change with temperature?

The minimum wavelength of electrons ejected from metal does not change with temperature. The work function of a metal is a constant value and is not affected by temperature. However, the number of electrons emitted from the metal surface may vary with temperature due to changes in the thermal energy of the electrons, which can affect their ability to overcome the work function barrier.

5. What factors can affect the minimum wavelength of electrons ejected from metal?

The minimum wavelength of electrons ejected from metal can be affected by several factors, including the type of metal, the intensity of the incident light, and the surface properties of the metal. The work function of a metal can also be influenced by external factors such as electric fields or the presence of impurities on the metal surface.

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