X rays have wavelengths on the order of 1 ×10^-10 m Calculate the energy of 1.0 ×10^-10 m X rays

X rays have wavelengths on the order of 1 ×10^-10 m...

X rays have wavelengths on the order of $1 \times 10^{-10} \mathrm{m}$ Calculate the energy of $1.0 \times 10^{-10} \mathrm{m}$ X rays in units of kilojoules per mole of $\mathrm{X}$ rays. AM radio waves have wavelengths on the order of $1 \times 10^{4} \mathrm{m}$. Calculate the energy of $1.0 \times 10^{4} \mathrm{m}$ radio waves in units of kilojoules per mole of radio waves. Consider that the bond energy of a carbon-carbon single bond found in organic compounds is $347 \mathrm{kJ} / \mathrm{mol}$. Would $\mathrm{X}$ rays and/or radio waves be able to disrupt organic compounds by breaking carbon-carbon single bonds?

Key Concepts

Chemical Bond Energy

Chemical bond energies, such as the energy required to break a carbon-carbon single bond, represent the amount of energy needed to disrupt those bonds in molecules. Comparing the energy of individual photons (or a mole of photons) to these bond energies helps determine whether radiation, based on its energy, can induce chemical reactions by breaking bonds in organic compounds.

Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance. By using Avogadro’s number, which is the number of particles in one mole, individual photon energies can be scaled up to obtain the energy per mole. This conversion is important in chemical calculations where energies are expressed per mole rather than per single photon.

Unit Conversion

In many scientific calculations, it is essential to convert energy units from joules to kilojoules or vice versa. This conversion facilitates comparison with other energy scales, such as chemical bond energies, which are often expressed in kilojoules per mole. Accurate unit conversion ensures that the computed photon energies are directly comparable to common chemical bond energies.

Planck's Equation

This is a fundamental equation in quantum mechanics that relates the energy of a photon to its wavelength (or frequency). It states that the energy (E) of a photon is equal to Planck’s constant (h) multiplied by the speed of light (c) and divided by the wavelength (?), succinctly expressed as E = hc/?. This equation is essential for converting the wavelength of electromagnetic radiation into its corresponding energy per photon.

Electromagnetic Spectrum

This concept encompasses the entire range of all types of electromagnetic radiation, classified by wavelength or frequency. X-rays and radio waves are two distinct regions within this spectrum, where X-rays have very short wavelengths and high energy, while radio waves have very long wavelengths and low energy. Understanding this spectrum is crucial when comparing the energy delivered by different types of radiation.

Transcript

00:01 In this problem, we have to find the energy of various levels of electromagnetic radiation.

00:08 And then we have to compare these energies in order to determine how would they, how they would react, pardon me, with organic compounds.

00:19 So the first thing that we'll do is we'll find the energy of the x -rays that we're given.

00:24 And for this problem, we're going to be using the energy for a photon equation, where we say e is equivalent to hc over lambda.

00:32 E is the energy of our photon, h is planks constant, c is the speed of light, and lambda is our wavelength in meters.

00:44 So for the x rays, we can say that the energy of the photon is equivalent to 6 .626 times 10 to the negative 34th joules seconds.

00:53 That's planx constant, times the speed of light, 3 times 10 to the 8th meters per second, divided by the wavelength, 1 times 10 to the negative 10 meters.

01:04 And when we simplify this, we'll get that the energy of the photon is 2 times 10 to the negative 15th joules.

01:14 And now what we'll want to do is convert these jewels into kilojoules.

01:20 So we can say that there are 2 times 10 to the negative 15th joules in every one photon.

01:28 And we should know that in every one mole, there are, avragadro's number of photons.

01:34 And then, in every one kilojoule, there are a thousand joules.

01:38 So we'll quickly do that calculation, and we'll get that the energy of the x -rays is 1 .2 times 10 to the 6th kilojoules per mole...

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