Questions: Name(print) 1. Ultraviolet light is divided into three categories, UV-A, UV-B, and UV-C. The wavelength ranges (in nanometers) are shown in the Figure. Hint: 1 m = 10^9 nm. (a) Which type of UV-radiation is most energetic? UV-C (b) Calculate the energy (in Joules) of one photon of UV-A radiation (any wavelength in its range).

Name(print)
1. Ultraviolet light is divided into three categories, UV-A, UV-B, and UV-C. The wavelength ranges (in nanometers) are shown in the Figure. Hint: 1 m = 10^9 nm.
(a) Which type of UV-radiation is most energetic?
UV-C
(b) Calculate the energy (in Joules) of one photon of UV-A radiation (any wavelength in its range).

Transcript text: Name(print) 1. Ultraviolet light is divided into three categories, UV-A, UV-B, and UV-C. The wavelength ranges (in nanometers) are shown in the Figure. Hint: $1 \mathrm{~m}=\mathbf{1 0}^{9} \mathrm{~nm}$. (a) Which type of UV-radiation is most energetic? $V V-C$ (b) Calculate the energy (in Joules) of one photon of UV-A radiation (any wavelength in its range).

Solution

Solution Steps

Step 1: Identify the most energetic type of UV radiation

UV radiation is divided into three categories: UV-A, UV-B, and UV-C.
The energy of radiation is inversely proportional to its wavelength.
UV-C has the shortest wavelength range (200-280 nm), making it the most energetic.

Final Answer

The most energetic type of UV radiation is UV-C.

Step 2: Determine the wavelength range for UV-A

UV-A radiation has a wavelength range of 315-400 nm.

Step 3: Calculate the energy of one photon of UV-A radiation

Use the formula $ E = \frac{hc}{\lambda} $, where:
- $ E $ is the energy of the photon,
- $ h $ is Planck's constant ($ 6.626 \times 10^{-34} $ J·s),
- $ c $ is the speed of light ($ 3.00 \times 10^8 $ m/s),
- $ \lambda $ is the wavelength in meters.
Choose a wavelength within the UV-A range, for example, 350 nm (which is $ 350 \times 10^{-9} $ m).

Step 4: Perform the calculation

Substitute the values into the formula: \[ E = \frac{(6.626 \times 10^{-34} \text{ J·s}) (3.00 \times 10^8 \text{ m/s})}{350 \times 10^{-9} \text{ m}} \] \[ E = \frac{1.9878 \times 10^{-25} \text{ J·m}}{350 \times 10^{-9} \text{ m}} \] \[ E = 5.68 \times 10^{-19} \text{ J} \]

Final Answer