What is the wavelength in nanometers of a photon with a frequency of 6.10 ✕ 10^14 sec-1? (The speed of light in a vacuum is 2.998 ✕ 108 m/s. Planck's constant is 6.626 ✕ 10^-34 J·s.)
I know that speed of light = wavelength * velocity, but I don't know what the velocity is. I don't need the answers necessarily, just an explanation please
I believe you are confused with the formula.
speed of light = frequency x wavelength
3E8 m/s = 6.10E14*wavelength
To find the wavelength of a photon, you can use the formula:
wavelength = speed of light / frequency
Given that the speed of light in a vacuum is 2.998 x 10^8 m/s and the frequency is 6.10 x 10^14 sec^-1, you can plug these values into the formula as follows:
wavelength = (2.998 x 10^8 m/s) / (6.10 x 10^14 sec^-1)
But first, you need to convert the frequency from sec^-1 to Hz (hertz) by simply removing the "sec^-1" unit:
wavelength = (2.998 x 10^8 m/s) / (6.10 x 10^14 Hz)
Now, divide the speed of light by the frequency:
wavelength = 4.911 x 10^-7 meters
Finally, you are asked to express the wavelength in nanometers. To convert meters to nanometers, you need to multiply by a conversion factor:
1 meter = 1 x 10^9 nanometers
Therefore, to convert from meters to nanometers, you multiply by 1 x 10^9:
wavelength = (4.911 x 10^-7 meters) * (1 x 10^9 nanometers / 1 meter)
Simplifying the expression, you get:
wavelength = 491.1 nanometers
So, the wavelength of the photon with a frequency of 6.10 x 10^14 sec^-1 is approximately 491.1 nanometers.