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.

answered above.

To calculate the wavelength, frequency, and energy of the absorbed radiation, we can use the speed of light (c) formula:

c = λν

Where:
c = speed of light (299,792,458 m/s or approximately 3.00 x 10^8 m/s)
λ = wavelength (in meters)
ν = frequency (in Hz)

First, let's convert the given wavenumber, 1953 cm^(-1), to meters by dividing by 100:

Wavenumber (in m^(-1)) = 1953 cm^(-1) / 100 = 19.53 m^(-1)

Now, we can use the speed of light formula to find the wavelength:

c = λν
λ = c / ν

To convert from meters to nanometers, we multiply the wavelength by 10^9:

λ (nm) = λ (m) x 10^9

Next, we need to find the frequency (ν). To do this, we rearrange the formula:

ν = c / λ

Finally, let's calculate the energy using the equation:

E = hν

Where:
E = energy (in Joules)
h = Planck's constant (6.626 x 10^(-34) J·s)
ν = frequency (in Hz)

Now, let's calculate the wavelength, frequency, and energy:

1. Calculate the wavelength (λ):

λ = c / ν
λ = (3.00 x 10^8 m/s) / (19.53 m^(-1))

Convert to nanometers:
λ (nm) = λ (m) x 10^9

2. Calculate the frequency (ν):

ν = c / λ

3. Calculate the energy (E):

E = hν

Substitute the given values for h and ν into the equation.

By following these steps, you should be able to calculate the wavelength (in nm), frequency, and energy of the absorbed radiation.