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

step 1 So in this, we're going to use the formula C is equal to wavelength, that's frequency. The speed

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

$\mathrm{X}$ rays have wavelengths on the order of $1 \times 10^{-10} \mathrm{~m} .$ Calculate the energy of $1.0 \times 10^{-10} \mathrm{~m} \mathrm{X}$ rays in units of kilojoules per mole of 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

Photon Energy

Photon energy is directly related to the wavelength of electromagnetic radiation, given by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This concept is crucial in understanding how different wavelengths correspond to different energy levels, with shorter wavelengths (like X-rays) having higher photon energies and longer wavelengths (like radio waves) having much lower energies.

Mole Concept and Avogadro's Number

In chemistry, energy values are often expressed per mole. By multiplying the energy of a single photon by Avogadro’s number, one can obtain the energy content per mole of photons. This conversion is essential for comparing photon energies with chemical bond energies, which are typically measured in kilojoules per mole.

Electromagnetic Spectrum

The electromagnetic spectrum covers a wide range of wavelengths and energies, from high-energy X-rays to low-energy radio waves. Understanding the distribution of energy across the spectrum helps in determining which forms of radiation are capable of causing chemical changes or disrupting molecular bonds.

Chemical Bond Energies

Chemical bonds, such as a carbon-carbon single bond, have characteristic bond energies that must be overcome to break the bond. By comparing the energy content per mole of electromagnetic radiation to these bond energies, one can assess whether the radiation (e.g., X-rays or radio waves) has enough energy to disrupt or break chemical bonds.

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