What is Photoelectric Effect?

Electrons can be liberated from a cool metal surface when light (electromagnetic radiation) of sufficiently high frequency is incident upon it. This phenomenon is known as the photoelectric effect.

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What are Photoelectrons?

Conduction electrons in the metal are bound to the lattice. The light beam provides the required energy for the electrons to break free from the metalic bonds. The liberated electrons are called photoelectrons.

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Rate and emission and KE of photoelectrons

Two important quantities provide clues for how light energy is delivered: (1) the rate of emission of photoelectrons, which is the number of photoelectrons emitted per unit time, and (2) the kinetic energy of the photoelectrons.

It’s important to grasp the difference between “rate” and “speed”. For example, the photoelectrons on the left are emitted at higher rate, but at lower speed compared to those on the right.

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Photoelectric Current

The experimental set-up to study the photoelectric effect consists of the emitter plate (from which photoelectrons are emitted) and a collector plate (at which photoelectrons are collected). When connected with a piece of wire and a microammeter, the microammeter measures a current. This current is called the photoelectric current.

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Saturation Current

Without any bias voltage, only a fraction of the photoelectrons that leave the plates arrive at the collector.

If we connect a battery between the emitter and the collector such that the collector is at a higher potential than the emitter, we establish what’s called a positive bias between the plates. A positive bias produces an electric field between the plates that attracts photoelectrons towards the collect.

Increasing the positive bias thus increases the percentage of photoelectrons collected, resulting in a higher and higher photoelectric current. The maximum is reached when every single photoelectron is collected. The maximum photoelectric current is called the saturation current I_sat.

The saturation current can be used to calculate the rate of emission of photoelectrons because

For example, a saturation current of 1.2 uA would imply an emission rate of 7.5 x 10¹² photoelectrons per second.

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Stopping Potential

If we connect the battery such that the collector is at a lower potential than the emitter, we establish what’s called a negative bias between the plates. A negative bias produces an electric field between the plates that repels photoelectrons away from the collect.

So photoelectrons must gain electric potential energy at the expense of losing kinetic energy as they travel towards the collector. For example, if there is a negative bias of 3 V, a photoelectron must lose 3 eV of KE in order to gain 3 eV of EPE if it were to reach the collect. This implies that only photoelectrons with initial KE ≥ 3 eV can arrive at the collector. Those with initial KE < 3 eV will be turned back before reaching the collector.

As photoelectrons are emitted with a range of KE, increasing the negative bias results in less and less photoelectrons arriving at the collector, and thus lower and lower photoelectric current, until the current becomes zero when even the most energetic photoelectron does not have sufficient initial KE to overcome the potential energy barrier between the plates. The negative bias at which this occurs is called the stopping potential V_s.

The stopping potential can be used to calculate the maximum KE of photoelectrons because

eV_s = KE_max

For example, a stopping potential of 1.3 V would imply a KE_max of 1.3 eV.

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I–V graph

Shown above is a typical I–V graph for a photoelectric experiment. It shows the variation of the photoelectric current against the bias voltage. The two important pieces of information provided by an I-V graph are (1) the saturation current, which allows us to calculate the rate of emission of photoelectrons, and (2) the stopping potential V_s which allows us to calculate the KE_max  of photoelections.

Finally, we are ready to examine the many surprises the photoelectric effect has in store for us.

• 18 Quantum Physics