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Chapter 6: Problem 26

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of \(941 \mathrm{~kJ} / \mathrm{mol}\) is required to break the nitrogen-nitrogen bond in \(\mathrm{N}_{2}\). What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Short Answer

Expert verified
The longest wavelength of radiation that can break the N-N bond in N2 molecule is \( 1273 \mathrm{nm} \), and it is Infrared radiation.

Step by step solution

01

Convert bond energy to joules per photon

As the given energy is in kJ/mol, we need to convert it into joules per photon. Since we know there are Avogadro's number (6.022 x 10^23) of photons in one mole, we'll divide the bond energy by Avogadro's number. Energy per mol = 941 kJ/mol = 941 x 10^3 J/mol Now, divide this by Avogadro's number to get the energy per photon: Energy per photon = \( \frac{941 \times 10^3 \mathrm{J/mol} }{ 6.022 \times 10^{23} \mathrm{mol^{-1}}} = 1.563 \times 10^{-19} \mathrm{J} \)
02

Use Planck's equation to find frequency

Planck's equation is \( E = h\nu \), where E is the energy, h is Planck's constant (6.626 x 10^-34 J s), and \( \nu \) is the frequency. To find the frequency, divide the energy per photon by Planck's constant : \( \nu = \frac{E}{h} \) \( \nu = \frac{1.563 \times 10^{-19} \mathrm{J}}{6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}} = 2.358 \times 10^{14} \mathrm{s}^{-1} \)
03

Use the speed of light equation to find the wavelength

The speed of light equation is \( c = \lambda\nu \), where c is the speed of light (3 x 10^8 m/s), \( \lambda\) is the wavelength, and \( \nu \) is the frequency. To find the wavelength, divide the speed of light by the frequency: \( \lambda = \frac{c}{\nu} \) \( \lambda = \frac{3 \times 10^8 \mathrm{m/s}}{2.358 \times 10^{14} \mathrm{s}^{-1}} = 1.273 \times 10^{-6} \mathrm{m} = 1273 \mathrm{nm} \)
04

Determine the type of electromagnetic radiation

Compare the wavelength to the range of wavelengths for each type of electromagnetic radiation: - Infrared: 700 nm to 1 mm - Visible: 400 nm to 700 nm - Ultraviolet: 10 nm to 400 nm Since the wavelength is within the infrared range, the radiation type is Infrared. Therefore, the longest wavelength of radiation that can break the N-N bond in N2 molecule is 1273 nm, and it is Infrared radiation.

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Most popular questions from this chapter

(a) State the Pauli exclusion principle in your own words. (b) The Pauli exclusion principle is, in an important sense, the key to understanding the periodic table. Explain why.

Determine which of the following statements are false, and correct them. (a) Electromagnetic radiation is incapable of passing through water. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

Sodium metal requires a photon with a minimum energy of \(4.41 \times 10^{-19} \mathrm{~J}\) to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect? (b) What is the wavelength of this light? (c) If sodium is irradiated with light of \(439 \mathrm{~nm}\), what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is \(1.00 \mu \mathrm{J} ?\)

Sketch the shape and orientation of the following types of orbitals: (a) \(p_{x}\), (b) \(d_{z^{2}}\),(c) \(d_{x^{2}-y^{2}}\).

An electron is accelerated through an electric potential to a kinetic energy of \(18.6 \mathrm{keV}\). What is its characteristic wavelength? [Hint: Recall that the kinetic energy of a moving object is \(E=\frac{1}{2} m v^{2}\), where \(m\) is the mass of the object and \(\nu\) is the speed of the object.]
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