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Chapter 18: Problem 17

The dissociation energy of a carbon-bromine bond is typically about 276 \(\mathrm{kJ} / \mathrm{mol}\) . (a) What is the maximum wave-length of photons that can cause \(\mathrm{C}-\) 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
To find the maximum wavelength of photons that can cause the C-Br bond dissociation, we first convert the dissociation energy to Joules per photon: Energy per photon (J) = (276 kJ per mol) * (1000 J per kJ) / (Avogadro's number, \(6.022\times10^{23}\) mol−1). Then, we use the Planck's equation \(\lambda = \frac{hc}{E}\) and plug in the values for \(E\), \(h\), and \(c\) to calculate the maximum wavelength \(\lambda\). Finally, we compare the calculated wavelength with the ranges of ultraviolet (10 nm - 400 nm), visible (400 nm - 700 nm), and infrared (700 nm - 1 mm) radiation to identify the type of radiation it corresponds to.

Step by step solution

01

Convert energy into Joules per photon

We are given the dissociation energy of the carbon-bromine bond as 276 kJ/mol, but we need it in Joules per photon. Since 1 mol consists of Avogadro's number of particles, we need to divide the given energy by Avogadro's number to get the energy per photon. We must also convert kJ to Joules by multiplying by 1000. Energy per photon (J) = (276 kJ per mol) * (1000 J per kJ) / (Avogadro's number, \(6.022\times10^{23}\) mol−1)
02

Calculate the maximum wavelength using Planck's equation

Planck's equation relates the energy of a photon to its wavelength: \(E = h\frac{c}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant (\(6.626\times10^{-34}\) Js), \(c\) is the speed of light (\(3 \times 10^8\) m/s), and \(\lambda\) is the wavelength. To find the maximum wavelength, we need to rearrange Planck's equation for \(\lambda\): \(\lambda = \frac{hc}{E}\) Now, plug in the values for \(E\), \(h\), and \(c\), and calculate the maximum wavelength \(\lambda\).
03

Identify the corresponding electromagnetic radiation

Based on the calculated wavelength, determine whether it corresponds to ultraviolet, visible, or infrared radiation: - Ultraviolet (UV) radiation: 10 nm - 400 nm - Visible light: 400 nm - 700 nm - Infrared (IR) radiation: 700 nm - 1 mm Compare the calculated wavelength with these ranges to identify the type of radiation.

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