Photoelectric Effect: Work Function and Stopping Voltage

[alciefrederic]

1. Two separate photocells are set up, using light sources with identical intensity and frequency, but with different metal cathodes, having different work functions. Which of these following are correct (more than 1 answer possible):
A. The stopping Voltage will be identical
B: The photoelectric current will be identical
C: The smaller the work function, the larger stopping voltage
D: The larger the work function, the larger maximum kinetic energy of photon electrons

Well, the answers in the book are available, which are B and C. C is reasonable, since E(e) = hf - W (W = workfunction), the smaller W is, the larger E(e) and so, the larger stopping voltage neccessary. However, B is doubtful, since according to:
E(e) = 0.5mv^2 = hf - W, the smaller the work function is, the higher the speed of electrons, so shouldn't the current produced be larger? (f constant here). (Since current I = q/t, the number of charges passing a particular passage over time, current depends on both speed of electrons and the actual numbers of electrons moving, doesn't it?.)
My textbook (Heinemann Physics 12, 3rd ed., VCE Australia, some of you who come from Australia may know of it) does not mention anything about increasing frequency = increasing current, while http://en.wikipedia.org/wiki/Photoelectric_effect claims it to be true. Looking for your thoughts, thanks.

Homework Equations

The Attempt at a Solution

 

[jbsteele]

Yes, increasing the frequency will increase the current. The photoelectric current is proportional to the number of photons that are incident on the cathode. As the frequency increases, more photons will be incident on the cathode, thus increasing the photoelectric current. Additionally, since the kinetic energy of the electrons is proportional to the frequency, increasing the frequency will result in electrons with greater kinetic energies, which will also increase the current.

 

[tomcue]

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to light of a certain frequency. The work function is the minimum amount of energy needed to remove an electron from the surface of the material. The stopping voltage is the minimum voltage needed to stop the electrons from reaching the anode.

Based on the given information, it is correct to say that the stopping voltage will be identical for both photocells. This is because the intensity and frequency of the light sources are the same, so the energy of the photons hitting the cathodes will be the same. This means that the work function will be the only factor affecting the stopping voltage, and since it is different for each cathode, the stopping voltage will also be different.

It is also correct to say that the smaller the work function, the larger the stopping voltage. This is because the stopping voltage is directly related to the energy of the electrons, which is dependent on the work function. A smaller work function means that less energy is needed to remove the electrons, so the remaining energy can be used to accelerate the electrons, resulting in a higher stopping voltage.

However, it is not necessarily true that the photoelectric current will be identical for both photocells. This is because the current depends not only on the speed of the electrons, but also on the number of electrons being emitted. While a smaller work function may result in higher speed electrons, it does not necessarily mean that more electrons will be emitted. This is because the number of electrons emitted is also dependent on the intensity of the light source, and it is not specified whether the intensity is the same for both photocells.

In terms of increasing frequency resulting in an increase in current, this is a valid statement. According to the equation E(e) = hf - W, the energy of the electrons is directly proportional to the frequency of the light. This means that as the frequency increases, the energy of the electrons also increases, resulting in a higher photoelectric current. However, this is assuming that all other factors such as intensity and work function remain constant.

Overall, it is important to consider all factors when studying the photoelectric effect, and to understand that the relationship between these variables is not always straightforward. The photoelectric effect is a complex phenomenon and further research and experimentation is needed to fully understand its intricacies.