Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies.
a) The C---O bond absorbs radiation of wavelength 9.6um. What frequency (in s-1) corresponds to that wavelength?
b) The H---Cl bond has a frequency of vibration of 8.652x10^13 Hz. What wavelength (in um) corresponds to that frequency?
speed of light in m/s = wavelength in m x frequency in hz.
That will do both problems.
3.10X10^5
a) To determine the frequency (ν) corresponding to a given wavelength (λ), we can use the formula:
ν = c / λ
where c is the speed of light (approximately 3.00 x 10^8 m/s).
First, we need to convert the wavelength from micrometers (μm) to meters (m) since the speed of light is given in meters per second:
9.6 μm = 9.6 x 10^(-6) m
Now, we can substitute the values into the formula:
ν = (3.00 x 10^8 m/s) / (9.6 x 10^(-6) m) = 3.13 x 10^13 s^(-1)
Therefore, the frequency corresponding to a wavelength of 9.6 μm is approximately 3.13 x 10^13 s^(-1).
b) To determine the wavelength (λ) corresponding to a given frequency (ν), we can rearrange the formula:
λ = c / ν
Substituting the given frequency into the formula:
λ = (3.00 x 10^8 m/s) / (8.652 x 10^13 s^(-1)) = 3.47 x 10^(-6) m
Finally, we need to convert the wavelength from meters (m) to micrometers (μm):
λ = 3.47 x 10^(-6) m = 3.47 μm
Therefore, the wavelength corresponding to a frequency of 8.652 x 10^13 Hz is approximately 3.47 μm.
To answer these questions, we need to use the relationship between wavelength, frequency, and the speed of light. The speed of light, denoted by "c," is approximately 3.00 x 10^8 meters per second.
a) To find the frequency corresponding to a given wavelength, we can use the formula:
Frequency = speed of light / wavelength
First, we need to convert the wavelength given in micrometers (um) to meters (m):
9.6 um = 9.6 x 10^-6 m
Now we can calculate the frequency using the formula:
Frequency = 3.00 x 10^8 m/s / 9.6 x 10^-6 m
Frequency ≈ 3.13 x 10^13 Hz
Therefore, the frequency corresponding to a wavelength of 9.6 um is approximately 3.13 x 10^13 Hz.
b) To find the wavelength corresponding to a given frequency, we can rearrange the formula:
Wavelength = speed of light / frequency
Given the frequency, we can directly substitute it into the formula:
Wavelength = 3.00 x 10^8 m/s / (8.652 x 10^13 Hz)
Wavelength ≈ 3.47 x 10^-6 m
To convert this wavelength from meters to micrometers (um), multiply by 10^6:
Wavelength ≈ 3.47 um
Therefore, the wavelength corresponding to a frequency of 8.652 x 10^13 Hz is approximately 3.47 um.