The greater the work function for a metal,
A) the greater the speed of the ejected electron
B) the smaller the speed of the ejected electron
C) the more electrons are ejected
D) the lower the threshold frequency
E) none of the above
To determine the answer, we need to understand what the work function of a metal refers to. The work function is the minimum amount of energy required to remove an electron from the surface of a material. It is measured in electron volts (eV).
By applying the concept of energy conservation, we can conclude that the speed of the ejected electron is determined by the energy it gains after being emitted. This energy is provided by the incident photons in the form of photoelectric effect.
When light with a frequency greater than the threshold frequency is incident on a metal surface, electrons can be ejected. If the light's frequency is less than the threshold frequency, no electrons will be emitted.
Now, let's consider the answer options one by one:
A) The greater the work function for a metal, the greater the energy required to remove an electron. This means that the electrons which are ejected will have less energy, resulting in a smaller speed. Therefore, option A is incorrect.
B) As explained in option A, the smaller the energy of the ejected electron, the smaller the speed. So, option B is correct.
C) The number of electrons ejected is not directly related to the work function. It depends on the intensity of the incident light rather than the work function. Therefore, option C is incorrect.
D) The threshold frequency is the minimum frequency of light that can eject electrons from a metal surface. It is not affected by the work function. Therefore, option D is incorrect.
E) Since the correct answer is B, and none of the other options are correct, option E ("none of the above") is the correct choice.
In conclusion, the correct answer is E) none of the above. The greater the work function for a metal, the smaller the speed of the ejected electron.
A nonzero work function reduces the energy of the ejected electron. It also increases the photon energy and frequency needed to eject the electron.
Now ask yourself: What does that do to electron speed?