A minimum energy of 151 kJ is required to dissociate a mole of iodine molecules, I2. Calculate the wavelength of radiation that supplies this energy, assuming each bond beaks by absorbing one photon.
dE = hc/wavelength
To calculate the wavelength of the radiation that supplies the required energy to dissociate a mole of iodine molecules, we will use the equation relating energy and wavelength:
Energy (E) = hc/λ
Where:
E is the energy in joules,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light in a vacuum (2.998 x 10^8 m/s), and
λ is the wavelength of the radiation in meters.
First, let's convert the given energy into joules. We know that 1 kJ = 1000 J, so:
151 kJ = 151,000 J
Now we can rearrange the equation to solve for the wavelength:
λ = hc/E
Substituting the given values:
λ = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / 151,000 J
Calculating the numerator:
λ = (1.989148 x 10^-25 J·m/s) / 151,000 J
Simplifying:
λ = 1.319 x 10^-30 m
Thus, the wavelength of the radiation that supplies the required energy is approximately 1.319 x 10^-30 meters.