Photoelectric Effect ~ threshold frequency dependent on incident light?

[ldesai149]

Homework Statement

True/False: In the photoelectric effect, the cut-off (threshold) frequency depends on the intensity of incident light.

Homework Equations

hv = W + 1/2mv^2

v = W/h

The Attempt at a Solution

The threshold frequency depends on the wavelength of incident light but not the intensity (??)

 

[tiny-tim]

Hi ldesai149!

… not the intensity (??)

That's right …

the whole point of the experiment is that even if you reduce the intensity so that only one photon goes through at a time, that one photon still needs to have the threshold energy (or frequency)

The threshold frequency depends on the wavelength of incident light …

no, the threshold frequency is fixed …

you might as well say "the threshold frequency depends on the frequency of incident light"

or "the minimum height for joining the army depends on the person's height"

 

[epsilonjon]

I am a bit unclear on this process too. I never understood why an electron could not absorb the energy from several photons at the same instant and gain the required energy this way, rather than having to absorb from just a single photon at a time.

Thanks :-)

 

[thebiggerbang]

one can't think about the photoelectric effect in terms of classical physics where the intensity of light is proportional to the square of the amplitude of the wave.

In QM, one deals with light as individual packets of light. Imagine, one packet of light is able to interact with and excite one and only one electron. So, if it's energy ain't high enough (frequency below threshold freq) , it will not be able to eject the electron! However, increase in the intensity of light would just imply more number of incoming photons, and thus more electrons getting excited.
;)

 

[ZapperZ]

I am a bit unclear on this process too. I never understood why an electron could not absorb the energy from several photons at the same instant and gain the required energy this way, rather than having to absorb from just a single photon at a time.

Thanks :-)

The cross section for such absorption is extremely small (look up multiphoton photoemission). This means that it is of very low probability of happening. By the time the next photon comes along at the right location, there's a very good chance that the electron has decayed back to the lower energy state in the conduction band (the lifetime in the excited state in a metal is of the order of femtoseconds). So using ordinary light, as opposed to high-intensity laser, the intensity is too low to cause multiphoton photoemission. So such photoelectric effect using more than just one photon doesn't normally occur.

Zz.

 

[Saitama]

Hi Idesa149!

Did you completely check your equations?
You can write
"hv=W+1/2v^2" as:-

"hv=hv₀+1/2mv^2"

Now you see, the threshold frequency(v₀) depends on the frequency of incident light.

And as tiny-tim stated, threshold frequency is fixed for a particular metal. That is, if you incident a light with a lower frequency and that too with a large intensity, a single elctron wouldn't be emitted.

 

[Ashu2912]

(1) Threshhold frequency is the characteristic of the metal, it does not depend on the radiation in any way.
(2) If you mean that why does the photoelectric effect's occurrence itself depend on the frequency of the radiation/ incident light and not on the intensity, then it is a correct statement.
(3) This is because the minimum energy needed to knock-out an electron is fixed, i.e. the threshold energy, corresponding to the threshold frequency, and one quanta of energy and the energy of one photon of radiation is fixed, depending upon it's frequency only. So, even if you "throw" as many photons of radiation as you can, electrons won't be emitted, as not even one of those photons has sufficient energy to take out an electron.
(4) Intensity is related to the number of such photons, of equal energy. The more the intensity/brightness, the more the number of photons. However, as said before, even if you have a very intense light but of insufficient frequency, photons won't be emitted.
Think of it in this way:
"The battle is one-on-one. So even if you have a large army of weak soldiers against the strongest soldier from the opposite kingdom, the larger army loses. Why, because none of them individually matches the stronger soldier..."