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Chapter 18: Problem 17

The dissociation energy of a carbon-bromine bond is typically about \(210 \mathrm{~kJ} / \mathrm{mol}\). (a) What is the maximum wavelength of photons that can cause \(\mathrm{C}-\mathrm{Br}\) bond dissociation? (b) Which kind of electromagnetic radiation-ultraviolet, visible, or infrared-does the wavelength you calculated in part (a) correspond to?

Short Answer

Expert verified
The maximum wavelength of photons that can cause C-Br bond dissociation is \(5.69 \times 10^{-7}\) m or 569 nm, which corresponds to visible electromagnetic radiation.

Step by step solution

01

Use the energy-wavelength relationship for photons

Recall the energy-wavelength relationship for photons given by the Planck's equation: \[E = h \frac{c}{\lambda}\] where E is the energy of the photon, h is the Planck's constant (\(6.63 \times 10^{-34} \mathrm{~Js}\)), c is the speed of light (\(3.00 \times 10^8 \mathrm{~m/s}\)), and λ is the wavelength of the photon. We are given the dissociation energy of the C-Br bond, which is \(210 \mathrm{~kJ/mol}\). We will first convert this energy into Joules and then into energy per photon using Avogadro's constant (number of entities per mol: \(6.022 \times 10^{23} \mathrm{~entities/mol}\)).
02

Convert the dissociation energy to Joules per photon

To convert the dissociation energy to Joules per photon, we can follow the steps below: 1. Multiply by 1000 to convert kJ to J: \(210 \mathrm{~kJ/mol} \times 1000 = 210,000 \mathrm{~J/mol}\) 2. Divide by Avogadro's constant to get J per photon: \(\frac{210,000 \mathrm{~J/mol}}{6.022 \times 10^{23} \mathrm{~entities/mol}} = 3.49 \times 10^{-19} \mathrm{~J/photon}\) Therefore, the dissociation energy per photon is \(3.49 \times 10^{-19} \mathrm{J}\).
03

Calculate the maximum wavelength

Now that we have the dissociation energy per photon (E), we can use the Planck's equation to find the maximum wavelength (λ): E = h(c/λ) → λ = hc/E Plugging in the values: λ = \(\frac{6.63 \times 10^{-34} \mathrm{~Js} \times 3.00 \times 10^8 \mathrm{~m/s}}{3.49 \times 10^{-19} \mathrm{~J}} = 5.69 \times 10^{-7}\) m The maximum wavelength of photons that can cause C-Br bond dissociation is \(5.69 \times 10^{-7}\) m or 569 nm.
04

Identify the type of electromagnetic radiation

Now we need to determine the type of electromagnetic radiation. The range of wavelengths for different types of electromagnetic radiation are: - Ultraviolet radiation: \(10 \; \mathrm{nm} \leq \lambda < 400 \; \mathrm{nm}\) - Visible radiation: \(400 \; \mathrm{nm} \leq \lambda < 750 \; \mathrm{nm}\) - Infrared radiation: \(\lambda \geq 750 \; \mathrm{nm}\) Since the calculated maximum wavelength (569 nm) falls within the range of visible radiation (\(400 \leq \lambda < 750\) nm), the type of electromagnetic radiation is visible light. So, the maximum wavelength of photons that can cause the C-Br bond dissociation is 569 nm, which corresponds to visible electromagnetic radiation.

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