# Calculating Max Electric Current in Photoelectric Cell

• Gabriel Maia
In summary, the problem involves 2.5×10^{15} photons with 2.5eV of energy hitting a photoelectric cell with a work function of 2.2eV. The photoelectric conversion efficiency is 20% and the maximum electric current can be found by multiplying the number of contributing photons (5×10^{14}) by the charge of a single electron (1.6×10^{-19}). The role of the external voltage is to adjust the stopping voltage, which is the difference between the photon energy and the work function. In a working system, a positive external plate is desired to draw electrons away. In the example of an ultrafast photo-electron gun, a high extraction voltage of -
Gabriel Maia
Hi. The problem is the following:

I have 2.5×10$^{15}$ photons inciding every second on a photoelectric cell. Each photon has 2.5eV of energy and the work function of the cell is 2.2eV. I know that the photoelectric conversion efficiency is 20% and I'm asked to find the maximum electric current through the cell when a potential difference V is aplied to the system.

So... I know that only 20% of the incoming photons will contribute to the current generation. That's 5×10$^{14}$ photons. It means that 5×10$^{14}$ photoelectrons will be taken away from the cell evey second. It is a current of

i=1.6×10$^{-19}$*5×10$^{14}$=8×10$^{-5}$ A

What is the role of V here? If the light has energy enough to take the photoelectrons, unless V=0.3eV (or anything >0.3eV) the potential will have no effect on the current, right?

Thank you.

If your external voltage is negative you can adjust it until the photocurrent stops - this "stopping voltage" is the difference between your photon energy (2.5 eV) and the work function (2.2 eV) ... so here it would be 0.3 V.

There is a more complex effect based upon the accumulation of low-energy electrons just above the emitting surface: it serves to blockade the continued electron emission, effectively increasing the value of the work function. So in a working system you want your external plate to be positive so that it draws the electrons away ... and with the highest field strength that does not arc so that the electrons are swept away more rapidly.

In my ultrafast photo-electron gun there are 1,000 pulses per second, each with ~1,000 to 10,000,000 electrons (adjustable and calibrated). The photon pulses are about 150 femtoseconds in duration, and the extraction voltage is -30,000 V on the cathode (grounded grid anode) placed 6 mm distant; this gives a field strength of 5,000,000 V/m, or 5 V/um. This setup is "fast" enough to avoid any electron buildup, and produces a train of electron pulses each of about 250 fs for the smallest bunches, and 400 fs for 10,000 electrons, etc.

## 1. What is a photoelectric cell?

A photoelectric cell is a type of device that converts light energy into electrical energy. It is made up of a metal surface, known as a cathode, and a positively charged metal plate, known as an anode. When light hits the cathode, it causes the emission of electrons, which are then attracted to the anode, creating an electric current.

## 2. How is the maximum electric current in a photoelectric cell calculated?

The maximum electric current in a photoelectric cell is calculated using the formula I = q/t, where I is the current, q is the charge, and t is the time. The charge, q, is equal to the number of electrons emitted from the cathode, which is dependent on the intensity of the light. The time, t, is the time it takes for the electrons to travel from the cathode to the anode.

## 3. What factors affect the maximum electric current in a photoelectric cell?

The maximum electric current in a photoelectric cell is affected by the intensity of the light, the energy of the photons in the light, the work function of the metal surface, and the distance between the cathode and the anode. Higher intensity light, higher energy photons, and a smaller distance between the cathode and anode will result in a higher maximum electric current.

## 4. Can the maximum electric current in a photoelectric cell be increased?

Yes, the maximum electric current in a photoelectric cell can be increased by increasing the intensity of the light, using light with higher energy photons, using a metal surface with a lower work function, and decreasing the distance between the cathode and anode. These factors will result in more electrons being emitted and a higher electric current.

## 5. How is the maximum electric current in a photoelectric cell used in practical applications?

The maximum electric current in a photoelectric cell is used in various practical applications, such as solar panels, light sensors, and photomultiplier tubes. In solar panels, the current produced by the photoelectric cell is utilized to power electrical devices. In light sensors, the current is used to detect the presence and intensity of light. In photomultiplier tubes, the current is amplified and used for detecting and measuring low levels of light.

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