One reason carbon monoxide (CO) is toxic in that it bind to the blood protein hemoglobin more
strongly than oxygen does. The hemoglobin – CO bond absorbs radiation of 1953 cm–1, which are in
units of wavenumbers. Wavenumber is defined as the reciprocal of wavelength, in units of cm.
Calculate the wavelength, in nm, frequency, and energy of the absorbed radiation.
1/wave number = wavelength in cm then convert to nm.
c = frequency x wavelength
delta E = h*frequency
delta E in joules, frequency in Hz, h is Planck's constant.
so it would be 1/1953 = 5.12e-4 cm and then just convert that to nm?
yes. When you convert wavelength to frequency, be aware that the formula is
USUALLY with c in meters/second (3 x 10^8 m/s) so you will need to convert to wavelength in meters to use that value for c. But once you have wavelength in nm, just multiply by 10^-9 and you will have meters.
To calculate the wavelength, frequency, and energy of the absorbed radiation, we can use the formula:
c = λν
Where:
c is the speed of light (approximately 2.998 × 10^8 m/s)
λ is the wavelength in meters (m)
ν is the frequency in hertz (Hz)
To convert from wavenumber (cm^(-1)) to wavelength (m), we use the formula:
λ = (1 / wavenumber) cm
Given that the wavenumber is 1953 cm^(-1), we can calculate the wavelength:
λ = (1 / 1953) cm = 5.12 × 10^(-4) cm
To convert the wavelength from cm to nm, we multiply by 10^7 (since there are 10^7 nm in 1 cm):
λ = 5.12 × 10^(-4) cm × 10^7 nm/cm = 512 nm
So the wavelength of the absorbed radiation is 512 nm.
To calculate the frequency, we use the formula:
ν = c / λ
ν = (2.998 × 10^8 m/s) / (5.12 × 10^(-4) m) = 5.86 × 10^11 Hz
Therefore, the frequency of the absorbed radiation is 5.86 × 10^11 Hz.
To calculate the energy of the absorbed radiation, we use the formula:
E = h * ν
Where:
E is the energy in joules (J)
h is Planck's constant (approximately 6.626 × 10^(-34) J·s)
E = (6.626 × 10^(-34) J·s) * (5.86 × 10^11 Hz) = 3.88 × 10^(-22) J
Since the energy value obtained is very small, it is more common to express it in electron volts (eV). To convert from joules to electron volts, we use the conversion factor:
1 eV = 1.602 × 10^(-19) J
E = (3.88 × 10^(-22) J) / (1.602 × 10^(-19) J/eV) = 0.242 eV
Therefore, the energy of the absorbed radiation is 0.242 eV.