Question

In a wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light?

Answer 1

Hint: Intensity is the energy transferred per unit area per unit time. Quantum is a packet of energy. The quanta of light are called photons. The energy of quantum is equal to Plank’s constant multiplied by frequency. The intensity in the quantum model is equal to photon flux per unit time.

Complete step by step answer:
It is true that in the wave picture of light, the intensity of the light is determined by the square of the amplitude. But the wave picture failed to explain the photoelectric effect. So, the concept of quantum was used by Einstein to explain it. We can understand that a quantum is nothing but a packet of energy. Energy of a quantum is given by $E=\dfrac{hc}{\lambda }$, where $h$ is Planck's constant, $c$ is velocity of light and $\lambda $ is the wavelength of the light.

As we know, the amplitude is defined as the power transported by the electromagnetic wave per unit area. According to Einstein, each photon (quantum of light energy) interacts with one electron, hence more the number of photons having energy higher than the threshold energy, more numbers of electrons.

It was noted that more is the intensity of light, a higher current will be observed in the photoelectric effect when the energy of photons is above the threshold energy. As the photons are a unit of energy and intensity of power transferred per unit area, we can now define the quantum picture of energy.
The intensity of light is the photon flux on the material per unit time.

Additional Information
The threshold energy depends on the nature of the material.
No matter how high is the intensity, if the energy of light photons is below the threshold energy of the material, no photoelectrons will be ejected in the photoelectric effect.
There are many quantities called light intensity, like luminous intensity and radiance.

Note:
Students can confuse the definition of intensity as energy per unit time but actually it is energy per unit area per unit time. Hence to avoid any confusion follow the definition of the physical quantity thoroughly.