Question

What is the photon energy of light with a wavelength of \(465 \mathrm{~nm}\) ? What type of radiation is this?

Short answer

The energy of the light with wavelength 465 nm is approximately \(3.18 \times 10^{-19}\) Joules. Since this wavelength falls within the visible light range (400-700 nm), it belongs to the visible radiation type.

Step-by-step solution

Convert Wavelength from nm to m

Convert the given wavelength from nanometers to meters by multiplying by \(1 \times 10^-9\). This yields \( λ=465 \times 10^-9 \ m \).

Calculate Energy

Substitute the values of \( h=6.626 \times 10^{-34} \ Js \), \( c=3 \times 10^{8} \ m/s \), and \( λ=465 \times 10^{-9} \ m \) into the Planck's equation \( E = \frac{hc}{λ} \) to find the energy of the photon.

Identify Type of Radiation

The corresponding energy range will dictate the type of radiation. Given the energy of the photon, compare with standard radiation types (e.g., radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) to identify the type of radiation. Visible light falls in the wavelength range 400-700 nm.

Key concepts

Wavelength Conversion

Understanding how to convert a wavelength, especially in exercises like calculating photon energy, is crucial for accuracy. Wavelengths are often given in nanometers (nm) because they naturally align with the scale at which light operates. However, scientific calculations typically require meters (m) to maintain consistency with the units for speed of light and Planck's constant. To convert from nanometers to meters, you multiply by a conversion factor:

• Multiply by \(1 \times 10^{-9}\) meters, which effectively shifts the decimal place 9 places to the left

Taking the given wavelength of \(465\) nm, converting it becomes:\[ λ = 465 \times 10^{-9} \ m \] Once converted, you can comfortably substitute it into equations requiring the Standard International (SI) units, making calculations smoother and more reliable.

Planck's Equation

Planck's equation is a cornerstone in understanding photon energy. It directly ties a photon's energy to its frequency or wavelength. Using the equation \( E = \frac{hc}{λ} \), one can calculate the energy of a photon when the wavelength is known. Here, each component plays a critical role:

• \(h\) is Planck’s constant, approximately \(6.626 \times 10^{-34} Js\).
• \(c\) is the speed of light, approximately \(3 \times 10^{8} m/s\).
• \(λ\) is the wavelength in meters.

Substituting these values, as we did for the wavelength of \(465 nm\) converted to meters, the energy calculation becomes very straightforward:\[ E = \frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{465 \times 10^{-9}} \] This yields the energy in joules, helping us quantify the energy of the light involved, a key aspect when delving into quantum physics and understanding radiation types.

Types of Radiation

Radiation comes in many forms, distinguished by their energy levels and wavelengths. Recognizing the types involves associating the calculated photon energy or its wavelength to known ranges:

• **Radio Waves**: Longest wavelengths and lowest energy.
• **Microwaves**: Shorter than radio waves and higher in energy.
• **Infrared**: Just below visible light, felt as heat.
• **Visible Light**: The only type visible to the human eye, ranging from about 400 nm to 700 nm.
• **Ultraviolet**: Shorter than visible light, can cause sunburns.
• **X-rays**: Used in medical imaging, higher energy than ultraviolet.
• **Gamma Rays**: Shortest wavelengths and highest energy, from nuclear reactions.

For the light with a wavelength of \(465\) nm, it's located in the **visible light spectrum**, specifically around the blue part. Identifying radiation type isn't just academic; it relates to its practical effects and uses in everyday technology and science.