Photoelectrons and Radiation Intensity Relationship

The question states a fundamental principle of the photoelectric effect: the photoelectric current is directly proportional to the number of photoelectrons emitted per second. Let's break down what this means.

The photoelectric current, often denoted by $I$, is essentially the flow of charge. This charge flow is carried by the photoelectrons that are ejected from a material when light shines on it.

The number of photoelectrons emitted per second is a measure of the rate at which electrons are ejected from the material. If more electrons are ejected each second, the rate of charge flow (current) will be higher.

Mathematically, this relationship can be expressed as:

Photoelectric Current ($I$) $\propto$ Number of photoelectrons emitted per second ($N$)

This means if you double the number of photoelectrons emitted per second, you double the photoelectric current, assuming other factors remain constant.

Connecting Intensity to Electron Emission

Now, let's consider the effect of the intensity of incident radiation (light) on this process.

• The intensity of light is related to the number of photons striking the surface per unit area per unit time.
• According to the principles of the photoelectric effect, each photon, if it has enough energy (greater than the work function of the material), can eject one photoelectron.
• Therefore, increasing the intensity of the incident light means more photons are hitting the surface every second.
• This leads to more photoelectrons being emitted from the surface per second, provided the photon energy is sufficient to overcome the work function.

This leads to the conclusion that the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.

Mathematically:

Number of photoelectrons emitted per second ($N$) $\propto$ Intensity of Incident Radiation

Implication of the Proportionality

Given that:

1. Photoelectric Current ($I$) $\propto$ Number of photoelectrons ($N$)
2. Number of photoelectrons ($N$) $\propto$ Intensity of Incident Radiation

It directly follows that the photoelectric current is also directly proportional to the intensity of the incident radiation. The statement in the question highlights the direct link between the measured current and the underlying rate of electron emission, which is controlled by the light's intensity.

Therefore, the implication is that the number of photoelectrons emitted per second increases proportionally as the intensity of the incident radiation increases.