Photoelectric Effect and atoms

In summary: So the energy is 4*\pi*r^2*c^2=h*nu*lambda. Thus the energy is 4*\pi*(100 cm)*(4 eV)*(1J)=-4*10-6J.In summary, an irradiating point source of light radiates 25 Watts at a wavelength of 5000 Angstroms. A metal plate will absorb this light and emit an electron when hit by a photon with enough energy. The time it takes for an electron to be emitted is 2.01 e-11 seconds.
  • #1
Domnu
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A monochromatic point source of light radiates 25 W at a wavelength of 5000 angstroms. A plate of metal is placed 100 cm from the source. Atoms in the metal have a radius of 1 angstrom. Assume that the atom can continually absorb light. The work function of the metal is 4 eV. How long is it before an electron is emitted from the metal?

I'm a bit confused here... when it says an atom can continually absorb light, does this mean that you can keep feeding it energy until it escapes from the metal? I'm assuming you can do this...

okay so the atom is 0.1 m away from the light source, so if you draw straight lines from the point source to the top and bottom of the atom, you get an isoceles triangle, two of the lengths which are (very close to) 0.1 m and the base which is just the diametre of the atom, 2 angstroms. Now, since the angle theta, which we define to be the vertex angle of this isoceles triangle, is extremely small, we can approximate it by saying

0.1 * sin theta = 2 e - 10
0.1 * theta = 2 e - 10
theta = 2 e - 9 rad

Now, this means that the atom receives

2e-9 / (2 pi) * 25 joules/sec of energy.

But a total of 4 eV is needed, so we have that the total time taken would be 2.01 e -11 sec.
 
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  • #2
Strange question.
Since it's a point source I think you should assume that the light goes into a sphere.
You can work out the J/s/m^2 at the target and so the photon/s/m^2.

The photo-electric effect says that you need 1 photon of the correct wavelength to emit an electron - unless you are going to do a QM calculation of the electron I can't see how you get the time - except just 'c' and 0,1m distance?
 
  • #3
Well, see, the thing is that one photon doesn't have enough energy to release the electron. So you need another photon (it is really strange, because this would never happen in reality... the question is hypothetical).
 
  • #4
[tex]4*\pi*r^{2}[/tex] is the surface area of a sphere. If the plate is a certain distance away, you can simply assume the the source is emitting isotropically. Divide the surface area of the plate by the spherical surface area (r= the distance from the plate). This will tell you what percentage of your photons are hitting the surface.

You can determine the energy departed by assuming the photon is completely absorbed (hence photoelectric absorption). The energy of a photon is [tex]E=h\nu[/tex] and [tex]c=\lambda\nu[/tex]. You probably need the density of the plate and some other things, but this should be enough to get you going.
 

1. What is the photoelectric effect?

The photoelectric effect is the phenomenon where electrons are emitted from a metal surface when light of a certain frequency shines on it.

2. How does the photoelectric effect support the particle nature of light?

The photoelectric effect supports the particle nature of light because it shows that light is made up of individual packets of energy, known as photons, that can interact with matter on a particle level.

3. What is the significance of the threshold frequency in the photoelectric effect?

The threshold frequency is the minimum frequency of light needed to cause the emission of electrons in the photoelectric effect. It is significant because if the frequency of light is below the threshold, no electrons will be emitted regardless of the intensity of the light.

4. How does the photoelectric effect explain the quantization of energy in atoms?

The photoelectric effect shows that the energy of electrons emitted from a metal surface is dependent on the frequency of light and not its intensity. This supports the idea that electrons in atoms can only exist at certain energy levels, and can only absorb or emit energy in discrete packets, or quanta.

5. What is the work function and how does it relate to the photoelectric effect?

The work function is the minimum amount of energy needed to remove an electron from the surface of a metal. It is directly related to the threshold frequency in the photoelectric effect, as the threshold frequency is equal to the work function divided by Planck's constant.

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