Question

One reason carbon monoxide (CO) is toxic is that it binds to the blood protein hemoglobin more strongly than oxygen does. The bond between hemoglobin and CO absorbs radiation of 1953 cm⁻¹ . (The units are the reciprocal of the wavelength in centimeters.) Calculate the wavelength (in nm and Å) and the frequency (in Hz) of the absorbed radiation.

Answer 1

Answer:

The wavelength in nm = 5120

The wavelength in A°= 51,200

The frequency of the absorbed radiation is $5.859\times 10^{13} Hertz$

Explanation:

1) The wave number of the CO bond = $\bar v=1953 cm^{-1}$

The wavelength corresponding to this wave number =$\lambda$

$\lambda =\frac{1}{\bar v}=\frac{1}{1953 cm^{-1}}=5.12\times 10^{-4} cm$

$1 cm = 10^7 nm$

$5.12\times 10^{-4}\times 10^7 nm=5120 nm$

$1 cm = 10^8 \AA$

$5.12\times 10^{-4}\times 10^8 \AA=51,200 \AA$

The wavelength in nm = 5120

The wavelength in A°= 51,200

2)

Wavelength of the wave = $\lambda =5120 nm = 5120\times 10^{-9} nm$

$1 nm = 10^{-9} m$

Frequecy of the wave = $\nu$

$\nu=\frac{c}{\lambda }$

c = Speed of light = $3\times 10^8 m/s$

$\nu=\frac{3\times 10^8 m/s}{5120\times 10^{-9} m}=5.859\times 10^{13} s^{-1}$

The frequency of the absorbed radiation is $5.859\times 10^{13} Hertz$

Answer 2

The bond between hemoglobin and CO absorbs radiation of 1953 cm⁻¹. The corresponding wavelength is 5120 nm and 51200 Å. The corresponding frequency is 5.855 × 10¹³ Hz.

The bond between hemoglobin and CO absorbs radiation of 1953 cm⁻¹, that is, the wavenumber (ν) is 1953 cm⁻¹.

We can calculate the wavelength (λ) using the following expression.

$\lambda = \frac{1}{\nu } = \frac{1}{1953cm^{-1} } = 5.120 \times 10^{-4} cm$

We will convert 5.120 × 10⁻⁴ cm to nm using the following conversion factors.

• 1 m = 100 cm.
• 1 m = 10⁹ nm.

$5.120 \times 10^{-4} cm \times \frac{1m}{100cm} \times \frac{10^{9}nm }{1m} = 5120 nm$

We will convert 5.120 × 10⁻⁴ cm to Å using the following conversion factors.

• 1 m = 100 cm.
• 1 m = 10¹⁰ Å.

$5.120 \times 10^{-4} cm \times \frac{1m}{100cm} \times \frac{10^{10}A }{1m} = 51200 nm$

We can calculate the frequency (f) of the absorbed radiation using the following expression.

$f = \frac{c}{\lambda } = \frac{2.998 \times 10^{8}m/s }{5.120\times 10^{-6}m } = 5.855 \times 10^{13} Hz$

where,

• c is the speed of light

The bond between hemoglobin and CO absorbs radiation of 1953 cm⁻¹. The corresponding wavelength is 5120 nm and 51200 Å. The corresponding frequency is 5.855 × 10¹³ Hz.

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