Question

The energy required to dissociate the Cl2 molecule to Cl atoms is 239 kJ/mol Cl2. If the dissociation of a Cl2 molecule were accomplished by the absorption of a single photon whose energy was exactly the quantity required, what would be its wavelength (in meters)?​

Answer 1

Step-by-step explanation:

The energy of a single photon can be calculated using the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength of the photon.

To dissociate one mole of Cl2 molecules, we need 239 kJ of energy. This corresponds to 239,000 J/mol of Cl2.

Now we can use the relationship between energy and the number of photons absorbed: E = Nhf, where N is the number of photons absorbed, h is Planck's constant, and f is the frequency of the absorbed photons.

We can relate the frequency of the absorbed photon to its wavelength using c = λf. Solving for f gives f = c/λ.

Combining these equations, we get E = Nh(c/λ), or N = E/(hc/λ). Substituting the value of E for the energy required to dissociate one mole of Cl2, we get:

N = (239,000 J/mol) / [(6.626 x 10^-34 J.s) x (2.998 x 10^8 m/s) / λ]

Solving for λ, we get:

λ = hc / (239,000 J/mol) = (6.626 x 10^-34 J.s x 2.998 x 10^8 m/s) / 239,000 J/mol

λ = 8.44 x 10^-7 m

Therefore, the wavelength of the photon required to dissociate one Cl2 molecule is approximately 8.44 x 10^-7 meters (or 844 nanometers).