Suppose you have a strong peak at 2230 cm–1. What is the wavelength of the radiation that was absorbed?
1/wavelength(in u) = wave number in cm-1.
Thanks!
To find the wavelength of the radiation that was absorbed, we can use the formula:
wavelength = speed of light / frequency
Where the speed of light is approximately 3.00 x 10^8 meters per second.
To convert the wavenumber into frequency, we can use the formula:
frequency = wavenumber x speed of light
Given that the wavenumber is 2230 cm^(-1), we need to convert it to meter^(-1) unit first:
wavenumber = 2230 cm^(-1) x (1 m / 100 cm)
wavenumber = 22.30 m^(-1)
Now that we have the wavenumber, we can calculate the frequency:
frequency = 22.30 m^(-1) x (3.00 x 10^8 m/s)
frequency ≈ 6.69 x 10^9 Hz
Finally, we can calculate the wavelength:
wavelength = (3.00 x 10^8 m/s) / (6.69 x 10^9 Hz)
wavelength ≈ 4.49 x 10^(-2) meters
Therefore, the wavelength of the absorbed radiation is approximately 4.49 x 10^(-2) meters.
To determine the wavelength of the radiation that was absorbed, we can use the equation:
c = λν
Where:
c = speed of light (approximately 3 × 10^8 m/s)
λ = wavelength of radiation (in meters)
ν = frequency of radiation (in Hz)
To convert the given wavenumber (2230 cm^−1) to frequency, we need to use the relationship:
ν = c/λ
To convert the wavenumber from cm^−1 to meters^−1, we divide by 100:
ν = (2230 cm^−1)/(100 cm/m) = 22.3 m^−1
Now we can solve for the wavelength by rearranging the equation:
λ = c/ν = (3 × 10^8 m/s)/(22.3 m^−1) = 1.35 × 10^7 m
Therefore, the wavelength of the radiation that was absorbed is approximately 1.35 × 10^7 meters.