The shortest wavelength of light capable of dissociating the Br-I bond in one molecule of iodine monobromide is 669 nanometers.
Given the following data:
- Bond energy = 179 kJ/mol.
Avogadro's number = [tex]6.02 \times 10^{23}[/tex]
Speed of light = [tex]3 \times 10^8\;meters[/tex]
Planck constant = [tex]6.626 \times 10^{-34}\;J.s[/tex]
To calculate the shortest wavelength of light capable of dissociating the Br-I bond in one molecule of iodine monobromide:
First of all, we would determine the energy in one molecule of iodine monobromide by using this formula:
[tex]Energy = \frac{Bond\;energy}{Avogadro's\;number} \\\\Energy = \frac{179 \times 10^3}{6.02 \times 10^{23}} \\\\Energy = 2.97 \times 10^{-19}\;Joules[/tex]
Now, we can calculate the shortest wavelength by using Einstein's equation for photon energy:
Mathematically, Einstein's equation for photon energy is given by the formula:
[tex]E = hf = h\frac{v}{\lambda}[/tex]
Where:
- [tex]\lambda[/tex] is the wavelength.
Substituting the given parameters into the formula, we have;
[tex]2.97 \times 10^{-19} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^{8}}{\lambda} \\\\\lambda=\frac{6.626 \times 10^{-34} \;\times\; 3.0 \times 10^{8}}{2.97 \times 10^{-19}} \\\\\lambda=\frac{1.99 \times 10^{-25} }{2.97 \times 10^{-19}}\\\\\lambda=6.69 \times 10^{-7} \\\\\lambda=669 \times 10^{-9}[/tex]
Shortest wavelength = 669 nanometers.
Note: [tex]1 \;nanometer = 1 \times 10^{-9} \;meter[/tex]
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