The portion of the electromagnetic spectrum that causes sunburn and skin cancer

Question

The portion of the electromagnetic spectrum that causes sunburn and skin cancer is the ultraviolet spectrum. ("Ultraviolet" means that portion with frequencies higher than violet.) We further break down this portion of hte spectrum into three types, by its wavelengths: UV-A, UV-B and UV-C. The dimensions of their wavelengths are roughly 400 to 320 nanometers (nm) for UV-A (linked with malignant melanomas); 320 to 290 nm for UV-B (primary cause of sunburn and skin cancer), and 290 to 200 nm for UV-C.

1) What is the highest frequency for radiation in the UV-A range? fUV-A-hi = ____ Hz

2) What is the lowest frequency for radiation in the UV-A range? fUV-A-low = ____ Hz

3) What is the highest frequency for radiation in the UV-B range? fUV-B-hi = ____ Hz

4) What is the lowest frequency for radiation in the UV-B range? fUV-B-low = ____ Hz

5) What is the highest frequency for radiation in the UV-C range? fUV-C-hi = ____ Hz

6) What is the lowest frequency for radiation in the UV-C range? fUV-C-low = ____ Hz

7) When an electromagnetic waves travels from on medium to another, the velocity of the waves may change, although the frequency will remain the same. (This change in velocity will have important implications in optics as we will soon learn.) Lets assume some sunlight containing UV-A radiation passes from air into water. The velocity of radiation in water is 75% of what it is in air. What is will be the largest wave length of the UV-A radiation once it has passed into the water? UV-A-long = ____ nm

8) What is will be the shortest wave length of the UV-A radiation once it has passed into the water? UV-A-short = ____ nm

Explanation / Answer

Velocity of UV Radiation is equal to the speed of light = 3.0 x 10^8 m/s

Now for UV - A, Wavelength range = 400 nm - 320 nm

Apply the formula, v = f x lemda => f = v/lemda

(1) Highest frequency for radiation in the UV-A range = (3.0x10^8)/(320x10^-9) = 9.37 x 10^14 Hz

(2) Lowest frequency for radiation in the UV-A range = (3.0x10^8)/(400x10^-9) = 7.5 x 10^14 Hz

UV - B, Wavelength range = 320 nm - 290 nm

(3) Highest frequency for radiation in the UV-B range = (3.0x10^8)/(290x10^-9) = 10.345 x 10^14 Hz

(4) Lowest frequency for radiation in the UV-B range = (3.0x10^8)/(320x10^-9) = 9.37 x 10^14 Hz

UV - C, Wavelength range = 290 nm - 200 nm

(5) Highest frequency for radiation in the UV-C range = (3.0x10^8)/(200x10^-9) = 1.50 x 10^15 Hz

(6) Lowest frequency for radiation in the UV-C range = (3.0x10^8)/(290x10^-9) = 10.345 x 10^14 Hz

Now, as per the condition, velocity of radiation in the water = 0.75x3.0x10^8 = 2.25 x 10^8 m/s

Again frequency remains constant

So, wavelength shall be directly proportional to velocity.

Therefore,

Largest wave length of the UV-A radiation once it has passed into the water = 0.75x400x10^-9 = 300 nm

Shortest wave length of the UV-A radiation once it has passed into the water = 0.75x320x10^-9 = 240 nm

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