Ultraviolet radiation and radiation of shorter wavelengths...

Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because these kinds of radiation carry enough energy to break bonds within the molecules. A typical carbon-carbon bond requires 348 $\mathrm{kJ} / \mathrm{mol}$ to break. What is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?

Key Concepts

Planck's Equation

Planck's equation, expressed as E = hc/?, defines the relationship between the energy (E) of a photon and its wavelength (?), with h representing Planck's constant and c the speed of light. This formula is fundamental to understanding how different wavelengths of electromagnetic radiation correspond to specific energy levels, which is critical in determining whether a photon has enough energy to initiate chemical reactions or break molecular bonds.

Bond Dissociation Energy

Bond dissociation energy is the amount of energy required to break a specific chemical bond in a molecule. It is typically expressed in energy per mole, establishing a threshold that light or other energy sources must meet or exceed to break the bond. This concept is key in fields like photochemistry and molecular physics, where assessing the energy from electromagnetic radiation against molecular bond strengths helps predict chemical behavior.

Unit Conversion from Mole to Photon Energy

In order to apply the energy-wavelength relationship to individual photons, it is necessary to convert the bond dissociation energy given per mole into the energy per single molecule. This is achieved by using Avogadro's number, which links the macroscopic energy units (kJ/mol) to microscopic energy scales appropriate for single photons, enabling careful comparison with the photon energy derived from Planck's equation.

Electromagnetic Radiation Spectrum

The electromagnetic radiation spectrum encompasses various types of radiation, from radio waves to gamma rays, each characterized by different wavelengths and energies. Understanding which segment of the spectrum, such as ultraviolet light, contains photons with sufficient energy to initiate processes like chemical bond breaking, is essential in applications spanning from material science to biological damage assessment.

Transcript

00:01 Hello people, how's it going? for this question, we're supposed to find the longest wavelength that is capable of breaking the carbon bond, which typically requires this amount of energy to break.

00:11 The energy is expressed in kilojoules per mode, so we have to do some unit conversion here.

00:16 But first, let's establish a relationship between wavelength and the energy.

00:21 First, i have energy equals to planes constant times new, which is the frequency.

00:28 I know the frequency can be expressed.

00:30 In terms of c over lambda, and now we arrange it to be expressed in terms of wavelength, and we're going to have lambda equals to h times c divided by e.

00:44 And that's the equation that we want.

00:46 Now we know the plan's constant, the speed of lagging the vacuum, and the energy as well.

00:51 But we have to convert the energy.

00:52 But first, plans constant 6 .63 times 10 to the power of negative 34, joules times second, and now speed of light, 3 times 10 to the power of 8 meters per second, all over 248 kilojoules per mole.

01:15 Now, if you do a quick examination, the unit here are not going to cancel on, right? so we have to do some unit conversion to make it convenient for us.

01:24 We know one kilojoules is 1 ,000 joules, right? and that's going to get rid of the killer jewels, leaving the jewels, which is appropriate for the juice here.

01:39 And then we have to convert the most...

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