Figure 1 shows an arrangement used to investigate the photoelectric effect - AQA - A-Level Physics - Question 2 - 2020 - Paper 1

The number of photoelectrons released per second corresponds to the maximum current measured in the circuit, given by the relationship:

$I = n e$

where:

• $I$ is the current,
• $n$ is the number of photoelectrons released per second, and
• $e$ is the elementary charge (approximately $1.6 \times 10^{-19}$ C).

At the maximum current, if, for instance, $I$ is given as $1.9 \mu A$, then:

1. Convert $I$ to amperes: $I = 1.9 \times 10^{-6} A$

2. Rearranging the equation gives: $n = \frac{I}{e} = \frac{1.9 \times 10^{-6}}{1.6 \times 10^{-19}} \approx 1.19 \times 10^{13} \text{ electrons per second}$

The current $I$ reaches a constant value for positive values of the potential difference $V$ because all emitted photoelectrons are effectively collected at the anode. When a positive potential is applied, it creates an electric field that accelerates the photoelectrons towards the anode. As the potential increases, more electrons are attracted, and eventually, a point is reached where all emitted electrons are captured, resulting in a saturated current. At saturation, the current no longer increases with further increases in $V$, hence it remains constant.

As the potential difference $V'$ becomes more negative, fewer photoelectrons can reach the anode due to the opposing electric field. The negative potential repels the electrons emitted from the photoemissive surface, reducing the number of electrons that can be collected. Consequently, this leads to a decrease in the measured current $I$. If the negative potential becomes sufficiently large, it may eventually prevent any emitted photoelectrons from reaching the anode, resulting in zero current.

When the investigation is repeated with a different photoemissive surface that has a smaller value of the work function $\phi$, the stopping potential will also change. The stopping potential is defined by the amount of potential needed to stop the most energetic photoelectrons from reaching the anode. Since the work function is lower, it implies that the energy of the emitted photoelectrons is higher for the same incident light frequency. Therefore, the required stopping potential decreases, as there are more energetic electrons that can be stopped with a lesser potential. As a result, the overall stopping potential will diminish when utilizing a material with a smaller work function.