iodine molecules dissociate into atoms aftr absorbin light of 4500 angstrom....if one quantum of radiation is absorbed by each molecule..calculate the kinetic energy of iodine atoms when bond energy is 24000joul per mole...

To tackle the problem of calculating the kinetic energy of iodine atoms after they absorb light, we need to break it down into manageable steps. The key points to consider are the bond energy of iodine molecules and the energy associated with the absorbed light. Let's go through this step by step.

Understanding the Basics

Iodine (I₂) molecules consist of two iodine atoms bonded together. When these molecules absorb light, they can dissociate into individual iodine atoms. The energy required to break this bond is known as the bond energy, which in this case is given as 24,000 joules per mole.

Energy of Light Absorption

The light absorbed by the iodine molecules has a wavelength of 4500 angstroms. To find the energy of the absorbed light, we can use the formula:

• E = (hc) / λ

Where:

• E is the energy of the photon (in joules),
• h is Planck's constant (approximately 6.626 x 10^-34 J·s),
• c is the speed of light (approximately 3.00 x 10⁸ m/s),
• λ is the wavelength of light (in meters).

First, we need to convert the wavelength from angstroms to meters:

• 4500 angstroms = 4500 x 10^-10 meters = 4.5 x 10^-7 meters.

Calculating the Energy of the Photon

Now, substituting the values into the energy formula:

• E = (6.626 x 10^-34 J·s * 3.00 x 10⁸ m/s) / (4.5 x 10^-7 m)

Calculating this gives:

• E ≈ 4.42 x 10^-19 joules per photon.

Relating Energy to Bond Energy

Since we know that one quantum of radiation is absorbed by each iodine molecule, we can now compare the energy of the absorbed photon to the bond energy. The bond energy of 24,000 joules per mole indicates how much energy is needed to dissociate one mole of iodine molecules into atoms.

Converting Bond Energy to Energy per Atom

To find the energy per iodine atom, we divide the bond energy by Avogadro's number (approximately 6.022 x 10²³ mol^-1):

• Energy per atom = 24,000 J/mol / (6.022 x 10²³ mol^-1) ≈ 3.98 x 10^-20 joules/atom.

Calculating Kinetic Energy

When the iodine molecule absorbs the photon, it gains energy. If the energy of the absorbed photon (4.42 x 10^-19 joules) is greater than the bond energy per atom (3.98 x 10^-20 joules), the excess energy will be converted into kinetic energy of the iodine atoms after dissociation.

Thus, the kinetic energy (KE) of the iodine atoms can be calculated as:

• KE = Energy of photon - Energy per atom

Substituting the values:

• KE = 4.42 x 10^-19 J - 3.98 x 10^-20 J ≈ 4.02 x 10^-19 joules.

Final Thoughts

The kinetic energy of each iodine atom after absorbing the light and dissociating from the molecule is approximately 4.02 x 10^-19 joules. This energy represents the motion of the atoms post-dissociation, illustrating how light energy can be transformed into kinetic energy in molecular systems.