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  1. Problems
  2. /A solution absorbs light of wavelength 620 nm…
MediumChemistryHigh School (11–12)The d- and f-Block Elements › Transition Elements (d-Block)NumericalA-LevelBoard ExamIB

A solution absorbs light of wavelength 620 nm…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A solution absorbs light of wavelength 620 nm620\ \text{nm}620 nm. Find the energy gap in kJ/mol that this matches. A second complex has an energy gap of 175 kJ/mol175\ \text{kJ/mol}175 kJ/mol. At what wavelength does it absorb? Use E=119 627/λE = 119\,627 / \lambdaE=119627/λ, with λ\lambdaλ in nm.

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Work it out on paper, then type your number. The answer itself stays hidden.

kJ/mol
nm
Need a reminder? The key ideaShowHide

Spin-only magnetic moment: μ=n(n+2) BM\mu = \sqrt{n(n+2)}\ \text{BM}μ=n(n+2)​ BM, with nnn unpaired electrons. An ion absorbs the light whose photon energy matches its d-d gap: E=119 627/λE = 119\,627 / \lambdaE=119627/λ in kJ/mol, with λ\lambdaλ in nm. An ion disproportionates if Ecell∘=E∘(reduced)−E∘(oxidised)E^\circ_{cell} = E^\circ(\text{reduced}) - E^\circ(\text{oxidised})Ecell∘​=E∘(reduced)−E∘(oxidised) is positive, and ΔG∘=−nFE∘\Delta G^\circ = -nFE^\circΔG∘=−nFE∘ with F=96 500 C/molF = 96\,500\ \text{C/mol}F=96500 C/mol.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The first gap. E=119 627620=192.9 kJ/molE = \dfrac{119\,627}{620} = 192.9\ \text{kJ/mol}E=620119627​=192.9 kJ/mol.

Step 2. The second wavelength. We want λ\lambdaλ, so λ=119 627E=119 627175=684 nm\lambda = \dfrac{119\,627}{E} = \dfrac{119\,627}{175} = 684\ \text{nm}λ=E119627​=175119627​=684 nm.

Answer: 192.9 kJ/mol192.9\ \text{kJ/mol}192.9 kJ/mol and 684 nm684\ \text{nm}684 nm.

Check. A longer wavelength means a smaller gap. Here 684 nm684\ \text{nm}684 nm is longer than 620 nm620\ \text{nm}620 nm, and 175 kJ/mol175\ \text{kJ/mol}175 kJ/mol is smaller than 192.9 kJ/mol192.9\ \text{kJ/mol}192.9 kJ/mol.

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