Question

Calculate the shortest wavelength of light capable of dissociating the Cl–F bond in one molecule of chlorine monofluoride if the bond energy, or bond dissociation energy, is 251 kJ/mol .

Answer 1

Answer:

477 nm

Explanation:

Using the expression for the energy as:

$E=\frac {h\times c}{\lambda}$

Where,  

h is Plank's constant having value $6.626\times 10^{-34}\ Js$

c is the speed of light having value $3\times 10^8\ m/s$

$\lambda$ is the wavelength of the light

Given, $Energy=251\ kJ/mol=251000\ J/mol$

Also, $N_a=6.023\times 10^{23}\ {mol}^{-1}$

So, Energy for one atom = $\frac{251000}{6.023\times 10^{23}}\ J$

Thus, applying values as:

$\frac{251000}{6.023\times 10^{23}}=\frac{6.626\times 10^{-34}\times 3\times 10^8}{\lambda}$

$251\times \:10^{26}\lambda=5^{20}\times \:125540965$

$\lambda=4.77\times 10^{-7}\ m=477\times 10^{-7}\ m=477\ nm$

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

Answer 2

The shortest wavelength of light capable of dissociating the Cl–F bond in one molecule of chlorine monofluoride is 475 nanometers.

Given the following data:

• Bond energy = 251 kJ/mol.

Based on science:

• Avogadro's number = $6.02 \times 10^{23}$

• Speed of light = $3 \times 10^8\;meters$

• Planck constant = $6.626 \times 10^{-34}\;J.s$

To calculate the shortest wavelength of light capable of dissociating the Cl–F bond in one molecule of chlorine monofluoride:

First of all, we would determine the energy in one molecule of chlorine monofluoride by using this formula:

$Energy = \frac{Bond\;energy}{Avogadro's\;number} \\\\Energy = \frac{251 \times 10^3}{6.02 \times 10^{23}} \\\\Energy = 4.17 \times 10^{-19}\;Joules$

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:

$E = hf = h\frac{v}{\lambda}$

Where:

• E is the energy.

• h is Planck constant.

• f is photon frequency.

• $\lambda$ is the wavelength.

• v is the speed of light.

Substituting the given parameters into the formula, we have;

$4.17 \times 10^{-19} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^{8}}{\lambda} \\\\\lambda=\frac{6.626 \times 10^{-34} \;\times\; 3.0 \times 10^{8}}{4.17 \times 10^{-19}} \\\\\lambda=\frac{1.99 \times 10^{-25} }{4.17 \times 10^{-19}}\\\\\lambda=4.75 \times 10^{-7} \\\\\lambda=475 \times 10^{-9}$

Shortest wavelength = 475 nanometers.

Note: $1 \;nanometer = 1 \times 10^{-9} \;meter$

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