Question

the intensity of the energy depends on waves. waves in waves. look at the inner \the visible light spectrum\ on the board.
a. what is the range of wavelengths for visible light?
b. what is the range of frequencies of visible light?

infrared:
wavelength:
frequency:

ultraviolet:
wavelength:
frequency:

x - rays:
wavelength:
frequency:

part about the suns harmful rays is partially visible but main questions are a - e (with infrared, ultraviolet, x - rays as sub - questions)

Explanation:

Part a: Visible Light Wavelength

Visible light wavelengths range from approximately 400 nanometers (nm) (violet) to 700 nm (red). This is a well - known range in the study of electromagnetic radiation, and it is the portion of the electromagnetic spectrum that human eyes can detect.

Part b: Visible Light Frequency

The frequency of visible light is related to its wavelength by the formula \( c=\lambda
u \) (where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \(
u \) is the frequency). Using \( c = 3\times10^{8}\space m/s \), for a wavelength of \( 400\space nm=400\times 10^{-9}\space m \), the frequency \(
u=\frac{c}{\lambda}=\frac{3\times 10^{8}}{400\times 10^{-9}}\approx7.5\times 10^{14}\space Hz \). For a wavelength of \( 700\space nm = 700\times10^{-9}\space m \), the frequency \(
u=\frac{3\times 10^{8}}{700\times 10^{-9}}\approx4.3\times 10^{14}\space Hz \). So the frequency range of visible light is approximately \( 4.3\times 10^{14}\space Hz \) to \( 7.5\times 10^{14}\space Hz \).

Part c: Infrared

• Wavelength: Infrared radiation has wavelengths longer than visible light. The wavelength range of infrared is approximately \( 700\space nm \) to \( 1\space mm \) (or \( 10^{6}\space nm \)).
• Frequency: Using the formula \( c=\lambda

u \), for \( \lambda = 700\space nm=700\times 10^{-9}\space m \), \(
u=\frac{3\times 10^{8}}{700\times 10^{-9}}\approx4.3\times 10^{14}\space Hz \), and for \( \lambda = 1\space mm = 1\times 10^{-3}\space m \), \(
u=\frac{3\times 10^{8}}{1\times 10^{-3}} = 3\times 10^{11}\space Hz \). So the frequency range of infrared is approximately \( 3\times 10^{11}\space Hz \) to \( 4.3\times 10^{14}\space Hz \).

Part d: Ultraviolet

• Wavelength: Ultraviolet radiation has wavelengths shorter than visible light. The wavelength range of ultraviolet is approximately \( 10\space nm \) to \( 400\space nm \).
• Frequency: Using \( c=\lambda

u \), for \( \lambda = 10\space nm = 10\times 10^{-9}\space m \), \(
u=\frac{3\times 10^{8}}{10\times 10^{-9}}=3\times 10^{16}\space Hz \), and for \( \lambda = 400\space nm=400\times 10^{-9}\space m \), \(
u=\frac{3\times 10^{8}}{400\times 10^{-9}}\approx7.5\times 10^{14}\space Hz \). So the frequency range of ultraviolet is approximately \( 7.5\times 10^{14}\space Hz \) to \( 3\times 10^{16}\space Hz \).

Part e: X - Rays

• Wavelength: X - rays have very short wavelengths. The wavelength range of X - rays is approximately \( 0.01\space nm \) to \( 10\space nm \).
• Frequency: Using \( c=\lambda

u \), for \( \lambda = 0.01\space nm=0.01\times 10^{-9}\space m \), \(
u=\frac{3\times 10^{8}}{0.01\times 10^{-9}} = 3\times 10^{19}\space Hz \), and for \( \lambda = 10\space nm=10\times 10^{-9}\space m \), \(
u=\frac{3\times 10^{8}}{10\times 10^{-9}}=3\times 10^{16}\space Hz \). So the frequency range of X - rays is approximately \( 3\times 10^{16}\space Hz \) to \( 3\times 10^{19}\space Hz \).

Harmful Sun Radiation

Some harmful radiations from the sun include ultraviolet (UV) radiation (which can cause skin cancer, sunburn, and damage to the eyes) and X - rays (though the sun emits relatively less X - ray radiation compared to UV, and excessive exposure to solar X - rays (during solar flares) can also be harmful to living organisms and electronic equipment in space). Also, gamma rays from the sun (during extreme solar events) can be harmful, but the sun's gamma ray emission is relatively rare and less intense compared to UV.

Answer:

a. Wavelength of visible light: \( 400\space nm - 700\space nm \)

b. Frequency of visible light: \( 4.3\times 10^{14}\space Hz - 7.5\times 10^{14}\space Hz \)

c. Infrared:

• Wavelength: \( 700\space nm - 1\space mm \)
• Frequency: \( 3\times 10^{11}\space Hz - 4.3\times 10^{14}\space Hz \)

d. Ultraviolet:

• Wavelength: \( 10\space nm - 400\space nm \)
• Frequency: \( 7.5\times 10^{14}\space Hz - 3\times 10^{16}\space Hz \)

e. X - Rays:

• Wavelength: \( 0.01\space nm - 10\space nm \)
• Frequency: \( 3\times 10^{16}\space Hz - 3\times 10^{19}\space Hz \)

Harmful radiation from the sun: Ultraviolet radiation (causes skin cancer, sunburn), X - rays (harmful during solar flares), Gamma rays (rare but harmful during extreme solar events)