Question 1

Multiple choiceMedium1 mark

An atom emits a photon during the transition shown in the energy-level diagram. Take h=6.6×10−34 J sh=6.6\times10^{-34}\,\text{J s} and c=3.0×108 m s−1c=3.0\times10^8\,\text{m s}^{-1} What is the wavelength of the emitted photon?

Energy, E / J5.0×10−19 J4.0×10−19 J3.0×10−19 J2.0×10−19 J1.0×10−19 J0 J0 J1.1×10−19 J4.4×10−19 J
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Answer: C. The photon energy equals the difference between the atomic energy levels. Using E=hfE=hf and c=fλc=f\lambda λ=hc/ΔE\lambda=hc/\Delta E

  1. ΔE=(4.4−1.1)×10−19=3.3×10−19 J\Delta E=(4.4-1.1)\times10^{-19}=3.3\times10^{-19}\,\text{J}
  2. λ=(6.6×10−34)(3.0×108)3.3×10−19=6.0×10−7 m\lambda=\frac{(6.6\times10^{-34})(3.0\times10^8)}{3.3\times10^{-19}}=6.0\times10^{-7}\,\text{m}

A: adds the two level energies instead of finding their difference.
B: uses the upper level’s energy relative to zero rather than the energy gap shown.
D: uses the lower level’s energy as the photon energy rather than the difference between the levels.

Remember: a spectral line corresponds to a photon with energy equal to the difference between two discrete atomic energy levels.

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