Chapter 9: Problem 2
The bond energy for a \(\mathrm{C}\) - C bond is about \(340 \mathrm{~kJ} / \mathrm{mol}, 600 \mathrm{~kJ} / \mathrm{mol}\) for \(\mathrm{C}=\mathrm{C}\), and \(400 \mathrm{~kJ} / \mathrm{mol}\) for \(\mathrm{C}-\mathrm{H}\). Calculate the energy/mol associated with X-ray radiation with wavelengths of \(0.585\) and \(1.54 \AA\). What does this imply about the stability of biomolecules in an X-ray beam?
Short Answer
Step by step solution
Convert Wavelength to Meters
Calculate Frequency Using the Speed of Light
Calculate Energy Using Planck’s Equation
Convert Energy to kJ/mol
Analyze Bond Stability Implication
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
X-ray radiation
There are harmful and beneficial uses of X-ray radiation:
- Medical diagnostics, including X-ray imaging and CT scans.
- Potential for tissue damage leading to mutations or cancer if overexposed.
- Industrial applications, such as examining the internal structure of complex machinery.
wavelength conversion
To convert angstroms to meters:
- Remember: 1 angstrom (\( \1 \AA\)) equals \(1 \times 10^{-10}\) meters.
Planck’s equation
This equation highlights key relationships:
- The higher the frequency, the greater the energy of the photon.
- Understanding photon energy is crucial in fields like quantum mechanics and chemistry.
biomolecular stability
Key aspects of biomolecular stability in relation to X-ray radiation include:
- Breaking of chemical bonds at energy levels higher than typical bond energies (e.g., \(340, 400, 600 \, \text{kJ/mol}\)).
- Potentially altering molecular structure, affecting biological functions.
- Necessity to manage X-ray exposure to minimize risk in medical and scientific settings.