The energy from radiation can be used to rupture chemical bonds. A minimum energy of 192 kJ/mol is required to break the bromine–bromine bond in Br2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Video transcript

Hey everyone, we're asked to calculate the longest wavelength of light that a carbon eel bond must be irradiated to bring it to the high energy vibrational state. And to determine where this lies in our spectrum. And we know that a car panel bond absorbs 20.54 kg joules per mole of energy. To answer this question, we need to use the following formula. Energy is equal to Planck's constant times our speed of light over our wavelength. Before we plug in our values, Let's go ahead and convert our energy of 20.54 kg per mole into jewels per photon, which is our unit for energy. Starting off with 20.54 kg jewels per one mole, We know that one mole contains 6.02, 2 times 10 to the 23rd photons, which is avocados number. And we want to convert our killer jewels into jewels and we have one kill a jewel Per 10 to the 3rd jewels. And when we calculate this, we end up with a value of 3.4, 1 times 10 to the negative 20 jewels over photons. Now we can go ahead and calculate for a wavelength using the formula above our wavelength is going to be equivalent to Plank's constant times our speed of light. All over our energy plugging in our values, we get 6.626 times 10 to the negative jewels times seconds, which is Plank's constant, Multiplied by our speed of light of 3.0 times 10 to the 8th m/s. And this is all going to be divided by the value we just calculated, which is 3.41 Times 10 to the negative jules over photons. And when we calculate this out, we end up with a value of 5.8-8 times 10 to the negative six meters and looking at our electromagnetic spectrum. This is going to be in our infrared region. So I hope this made sense and let us know if you have any questions.