ii is related to the energy the ejected electron has, not the number of electrons ejected. Higher intensity will result in an electron ejected with a greater potential energy.
if it is related to the energy of the electron then wouldnt an increase in f cause the energy to increase according to plancks quantum theory?
The total energy will in fact increase, but the increase will be in the average kinetic energy of the ejected electrons, not in the number of electrons. In other words, if you increase the frequency of the incident monochromatic light while maintaining the same intensity, then the number of ejected electrons will remain the same but they will be ejected faster.
hvincident = hvthreshold + 1/2mvelectron2
Choice two corresponds to increasing the energy of each photon coming from the source but maintaining the same number of photons. Since it's only necessary for a photon to have more energy than the work function for the metal and it does not matter how much more it is, increasing the energy of photons will not increase the number of electrons ejected.
This makes sense, but wouldnt an increase in 'average' energy also mean that the photons with less energy than the work function can now cause an electron to be emitted?
As milski stated, it is monochromatic light, so the increase in average energy per photon is another way of saying all of the incident photons are of equal energy to one another, but now those photons have more energy than in the first trial.
BR has a great way of thinking about the photoelectric effect. It's essentially like a vending maching.
(1) If you don't put enough money in, then you don't get an item (just your money back). The same is true for the incident photon's energy and the work function. If the photon has a energy below the
cost of the electron, then it won't be ejected.
(2) Once you put enough money in the vending maching, you get an item and change back if you put in an amount over the price. The same is true with the photoeletcric effect, where if the incident photon has more energy than the work function, then you get the item (an electron) and some change (kinetic energy of the electron).
(3) If you put in a larger denomination of money, you still only get one item, but you get more change back. If you put in a photon of high energy (higher frequency), you still only get one ejected electron, but it has more kinetic energy than before.
(4) To get more items from the vending machine, you have to do the event more often ($1 five times rather than $5 one time). To get more electrons from the metal, you have to do the event more often (strike the metal with more photons).
Hopefully this analogy clears things up.
