17.1.3 Saturation Current

Not all the photoelectrons arrive at the collector. Some are them land at the tube instead. Others may even return to the emitter. What can we do to guide these “lost” photoelectrons towards the collector?

As illustrated in the diagram, a bias voltage can be set up between the two plates by a variable DC power supply. When the collector is connected to the positive terminal of the power supply, it is said to be in positive bias. As we gradually increase the positive bias, the collector (being positively charged) becomes increasingly attractive to the (negatively charged) photoelectrons. As more and more of the photoelectrons are reabsorbed at the collector, the photoelectric current increases. However, once every single photoelectron that is emitted has been successfully collected, the photoelectric current saturates at a maximum value. This maximum current is called the saturation current, Is.

When the micro-ammeter shows that the photoelectric current has saturated, we know that the rate of arrival (of photoelectrons at the collector) is equal to the rate of emission (of photoelectrons at the emitter). This allows us to use Isat to calculate the rate of emission of photoelectrons \displaystyle \frac{N}{t} since

\displaystyle {{I}_{{sat}}}=\frac{Q}{t}=\frac{N}{t}e

Example

Calculate the rate of emission of photoelectrons for a 1.2 uA saturation current.

Solution

\displaystyle {{I}_{{sat}}}=\frac{N}{t}e\text{ }\Rightarrow \text{ }1.2\times {{10}^{{-6}}}=\frac{N}{t}(1.60\times {{10}^{{-19}}})\text{ }\Rightarrow \text{ }\frac{N}{t}=7.5\times {{10}^{{12}}}\text{ }{{\text{s}}^{{-1}}}

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