91Ó°ÊÓ

To find the wavelength of light given the energy of a photon, we can use the relationship between energy and wavelength: \[ E = \frac{hc}{\lambda} \]. This formula shows us how energy \( E \) relates to Planck's constant \( h \), the speed of light \( c \), and the wavelength \( \lambda \) of the light. By rearranging the equation, we can solve for wavelength \( \lambda \): \[ \lambda = \frac{hc}{E} \]. This tells us that the wavelength is directly related to \( h \) and \( c \), but inversely related to \( E \). This means higher energy results in a shorter wavelength and vice versa. Simply put, if you know the energy of the photon, you can calculate its wavelength by using this formula. It is just a matter of plugging in the known values and calculating using standard arithmetic. Here's how it works with our example:

• Planck's constant \( h = 6.63 \times 10^{-34} \) Js,
• speed of light \( c = 3 \times 10^8 \text{ m/s} \),
• energy \( E = 3.34 \times 10^{-19} \text{ J} \).

Substitute these values to find the wavelength \( \lambda \): \( \lambda = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{3.34 \times 10^{-19}} \approx 5.95 \times 10^{-7} \text{ meters} \). This calculation shows that the wavelength of the photon is approximately 595 nm. This is inside the range of light visible to the human eye.

Planck's constant is a fundamental constant in physics that plays a central role in quantum mechanics. It is symbolized by \( h \) and has a value of \( 6.63 \times 10^{-34} \text{ Js} \). This value is incredibly small, which makes sense given that it deals with the energy levels of tiny particles like photons. Planck's constant is crucial because it relates the energy of a photon to the frequency of its electromagnetic wave:

• The equation \( E = hf \) shows this relationship, where \( E \) is energy and \( f \) is the frequency.
• In our equation for finding wavelength, \( h \) is paired with the speed of light \( c \) to calculate the energy per photon according to its wavelength.

Without Planck's constant, we wouldn't be able to properly understand or calculate the properties of photons and their interaction with energy. It sets a scale for the quantization seen in many physical systems, ensuring our calculations align with real-world observations.

The visible spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye. Wavelengths within this range are perceived as different colors, where each wavelength corresponds to a specific color:

• Red light has longer wavelengths, roughly between 620 to 750 nm.
• Orange falls between 590 to 620 nm, hence a 595 nm light, like the one calculated in the exercise, is orange.
• Yellow ranges from 570 to 590 nm.
• Green spans 495 to 570 nm.
• Blue ranges from 450 to 495 nm.
• Violet has the shortest wavelengths, between 380 to 450 nm.

Knowing the wavelength of light and its position within the visible spectrum allows us to determine its color. This can be particularly useful in fields where color identification is crucial, such as in lighting design or optical technologies. Keep in mind, light just outside the visible spectrum remains invisible to the human eye; these include ultraviolet and infrared light.