Here is the question.
Medical X-rays, with a wavelength of about 10^-10m, can penetrate completely through your skin.
a. Ultraviolet rays, which cause sun burn by penetrating only the top level of skin, have a wavelength about 1000 times the wavelength of an x-ray. Find the wavelength of visible rays. Show your work.
b. the wavelengths of visible light are between 3.8 x 10^-7m and 7.6 x 10^-7m. Are these wavelengths longer or shorter than those of ultraviolet rays? Explain.
If anyone can help I would be forever greatful. I have been trying to figure this out for 2 days and have not had any luck.
a. L = 10^3 * 10^-10 = 10^-7 m.
b. The given wavelengths are 3.8 to 7.6 times ultraviolet rays.
a. To find the wavelength of visible rays, we know that the wavelength of medical X-rays is 10^-10m and the wavelength of ultraviolet rays is 1000 times that of X-rays.
Let's calculate the wavelength of ultraviolet rays first:
Wavelength of ultraviolet rays = 1000 * (wavelength of X-rays)
= 1000 * (10^-10m)
= 10^-7m
Now, we can find the wavelength of visible rays:
Wavelength of visible rays = (wavelength of ultraviolet rays) / 1000
= 10^-7m / 1000
= 10^-10^4m
= 10^-7m
Therefore, the wavelength of visible rays is approximately 10^-7m.
b. The given wavelengths of visible light are between 3.8 x 10^-7m and 7.6 x 10^-7m. Since the wavelength of ultraviolet rays is 10^-7m (as obtained in part a), we can see that the given wavelengths of visible light (between 3.8 x 10^-7m and 7.6 x 10^-7m) are longer than that of ultraviolet rays.
In summary, ultraviolet rays have shorter wavelengths than that of visible light.
a. To find the wavelength of visible rays, we can use the given information that the wavelength of medical X-rays is about 10^-10m and that ultraviolet rays have a wavelength about 1000 times the wavelength of an X-ray.
Let's start by finding the wavelength of ultraviolet rays:
Wavelength of ultraviolet rays = 1000 * wavelength of X-rays
= 1000 * 10^-10m
To find the wavelength of visible rays, we need to convert the above result to meters. Since 1 nanometer (nm) is equivalent to 10^-9m, we can multiply the result by 10^-9 to get the wavelength in meters:
Wavelength of ultraviolet rays = 1000 * 10^-10 * 10^-9m
= 1000 * 10^-19m
Since we know the wavelength of visible light is between 3.8 x 10^-7m and 7.6 x 10^-7m, we can conclude that the wavelength of visible rays is shorter than the calculated wavelength of ultraviolet rays.
b. The given range for the wavelength of visible light, 3.8 x 10^-7m to 7.6 x 10^-7m, is longer than the calculated wavelength of ultraviolet rays, which was roughly 1000 times larger and approximately 1000 x 10^-19m. Thus, visible light has a longer wavelength than ultraviolet rays.
To recap:
a. The wavelength of visible rays can be calculated using the given wavelength of X-rays and the information about ultraviolet rays.
b. The wavelengths of visible light are longer than those of ultraviolet rays, as indicated by the provided range and the calculation in part (a).