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Chapter 23: Problem 48

(a) A complex absorbs photons with an energy of 4.51 \(\times 10^{-19} \mathrm{J}\) . What is the wavelength of these photons? (b) If this is the only place in the visible spectrum where the complex absorbs light, what color would you expect the complex to be?

Short Answer

Expert verified
The wavelength of the absorbed photons is approximately \(441 \mathrm{nm}\), which falls within the violet range of the visible light spectrum. Therefore, we would expect the complex to appear violet in color.

Step by step solution

01

Identify the given information

We are given the energy of the absorbed photons as \(E = 4.51 \times 10^{-19} \mathrm{J}\)
02

Write down the energy-wavelength relationship

The formula to relate energy and wavelength is given by: \(E = \dfrac{hc}{\lambda}\) where h is the Planck's constant (\( h \approx 6.63 \times 10^{-34} \mathrm{Js}\)), c is the speed of light (\( c \approx 3 \times 10^{8} \mathrm{m/s}\)), and λ is the wavelength of the photons.
03

Solve for the wavelength λ

We can isolate λ as follows: \[\lambda = \dfrac{hc}{E}\] Now, plug in the given values of E, h, and c: \[\lambda = \dfrac{(6.63 \times 10^{-34} \mathrm{Js})(3 \times 10^{8} \mathrm{m/s})}{4.51 \times 10^{-19} \mathrm{J}}\]
04

Calculate the wavelength λ

After plugging in the values and solving for λ, we get: \[\lambda \approx 4.41 \times 10^{-7} \mathrm{m}\] or \(λ \approx 441 \mathrm{nm}\)
05

Determine the color of the complex

Using the calculated wavelength of \(441 \mathrm{nm}\), we can find the color corresponding to this wavelength. The visible light spectrum ranges from approximately 400 nm to 700 nm, with colors arranged as follows: violet: (380–450 nm), blue: (450-495 nm), green: (495–570 nm), yellow: (570–590 nm), orange: (590-620 nm), and red: (620–750 nm). The calculated wavelength of \(441 \mathrm{nm}\) falls in the violet range. So, we would expect the complex to appear violet in color.

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Most popular questions from this chapter

Consider the following three complexes: (Complex 1) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SCN}\right]^{2+}\) (Complex 2) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{2+}\) (Complex 3) \(\mathrm{CoClBr} \cdot 5 \mathrm{NH}_{3}\) Which of the three complexes can have (a) geometric isomers, (b) linkage isomers, (c) optical isomers, (d) coordination-sphere isomers?

A Cu electrode is immersed in a solution that is 1.00\(M\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) and 1.00 \(\mathrm{M}\) in \(\mathrm{NH}_{3} .\) When the cathode is a standard hydrogen electrode, the emf of the cell is found to be \(+0.08 \mathrm{V} .\) What is the formation constant for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\)

A manganese complex formed from a solution containing potassium bromide and oxalate ion is purified and analyzed. It contains \(10.0 \% \mathrm{Mn}, 28.6 \%\) potassium, \(8.8\%\) carbon, and 29.2\(\%\) bromine by mass. The remainder of the compound is oxygen. An aqueous solution of the complex has about the same electrical conductivity as an equimolar solution of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] .\) Write the formula of the compound, using brackets to denote the manganese and its coordination sphere.

A four-coordinate complex \(\mathrm{MA}_{2} \mathrm{B}_{2}\) is prepared and found to have two different isomers. Is it possible to determine from this information whether the complex is square planar or tetrahedral? If so, which is it?

Carbon monoxide, CO, is an important ligand in coordination chemistry. When \(\mathrm{CO}\) is reacted with nickel metal, the product is \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right],\) which is a toxic, pale yellow liquid. (a) What is the oxidation number for nickel in thiscompound? (b) Given that \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) is a diamagnetic molecule with a tetrahedral geometry, what is the electron configuration of nickel in this compound? (c) Write the name for \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) using the nomenclature rules for coordination compounds.
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