Assume that \(2 \times 10^{-17} \mathrm{~J}\) of light energy is needed by the interior of the human eye to see an object. How many photons of yellow light with \(\lambda=595.2 \mathrm{~nm}\) are needed to generate this minimum energy? (a) 6 (b) 30 (c) 45 (d) 60

Planck's constant, denoted as 'h', is a fundamental quantity in quantum mechanics. It links the amount of energy a photon has with the frequency of its associated electromagnetic wave. The exact value of Planck's constant is approximately \(6.626 \times 10^{-34}\) joule-seconds (Js).

Understanding Planck's constant is critical when calculating the energy of photons, as shown in the example problem. When we multiply Planck's constant by the speed of light and divide by the wavelength of the light, we obtain the energy of a single photon. This constant provides the bridge between the wave and particle views of light and is crucial for understanding phenomena at the microscopic scale, including how photons interact with matter, such as in the human eye to produce vision.

The wavelength of light, represented by \(\lambda\), is the distance between two consecutive peaks or troughs of a light wave. It's typically measured in nanometers (nm) when discussing the light visible to the human eye. Different wavelengths correspond to different colors; for instance, yellow light has a wavelength around 595.2 nm.

In the energy calculation for a photon, the wavelength inversely determines the energy: the shorter the wavelength, the higher the energy of the photon. Knowing the wavelength is essential for calculations involving the energy of light, as seen in our example where the wavelength of yellow light is crucial to determine the number of photons needed for vision.

The speed of light, denoted by 'c', is a constant value at approximately \(3 \times 10^{8}\) meters per second (m/s) in a vacuum. It's one of the most important constants in physics as it sets the limit for the maximum speed at which information or matter can be transferred through the universe.

In our photon energy calculation, we use the speed of light along with Planck's constant and the light's wavelength to determine the energy of a single photon. This triad of values is fundamental in understanding how light behaves both as a wave and a particle, impacting fields ranging from cosmology to communications technology.

Photons are the basic units or 'quanta' of light, responsible for carrying electromagnetic force. One way to visualize this is by imagining them as tiny packets of energy zipping around at the speed of light. When these photons enter the human eye, they interact with the rods and cones in the retina, triggering a biological response that results in vision.

The number of photons is directly proportional to the brightness we perceive. In the given example, to achieve the minimum threshold of energy for vision, multiple photons of yellow light are needed, as a single photon's energy is insufficient. By calculating the necessary number of photons, we can understand the interplay between light intensity and the human eye's sensitivity.