X-ray diffractometers often use metals that have had their cor...

Question

X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p → 1s transition for copper, which is called the K⍺ transition. Calculate the wavelength of X-rays (in Å) given off by the K⍺ transition if the energy given off by a mole of copper atoms is 7.77⨉10⁵ kJ.(1Å = 10^-10 m)

Accepted Answer

Identify the energy of the Ka transition for one mole of copper atoms, which is given as 7.77 \times 10^5 \text{ kJ/mol}.. Convert the energy from kJ to J by multiplying by 1000, since 1 \text{ kJ} = 1000 \text{ J}.. Use Avogadro's number (6.022 \times 10^{23} \text{ atoms/mol}) to find the energy of the transition for a single copper atom by dividing the total energy in joules by Avogadro's number.. Apply the energy-wavelength relationship using the formula $ E = \frac{hc}{\lambda} $, where $ E $ is the energy of a single photon, $ h $ is Planck's constant (6.626 \times 10^{-34} \text{ J s}), and $ c $ is the speed of light (3.00 \times 10^8 \text{ m/s}).. Solve for the wavelength $ \lambda $ in meters, and then convert it to angstroms by using the conversion factor 1 \text{ Å} = 10^{-10} \text{ m}.

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Key Concepts

X-ray Emission

Energy-Wavelength Relationship

Mole Concept and Energy Conversion