Ch.7 - Quantum-Mechanical Model of the Atom

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.7 - Quantum-Mechanical Model of the Atom

Problem 80

Chapter 7, Problem 80

The energy required to ionize sodium is 496 kJ/mol. What minimum frequency of light is required to ionize sodium?

Verified step by step guidance

First, understand that ionization energy is the energy required to remove an electron from an atom or ion. In this case, it's the energy needed to ionize sodium.

Convert the ionization energy from kilojoules per mole (kJ/mol) to joules per mole (J/mol) by multiplying the given value by 1000, since 1 kJ = 1000 J.

Use the formula for the energy of a photon, which is given by \(E = h \nu\), where \(E\) is the energy, \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) Js), and \(\nu\) is the frequency of the light.

Rearrange the formula to solve for the frequency, \(\nu = \frac{E}{h}\). Substitute the energy value you converted into joules per mole in step 2.

Since the energy provided is per mole, and Avogadro's number (\(6.022 \times 10^{23} \text{ mol}^{-1}\)) gives the number of particles per mole, divide the energy per photon by Avogadro's number to find the energy per photon, then use this value to find the frequency.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ionization Energy

Ionization energy is the amount of energy needed to remove an electron from an atom or ion in its gaseous state. For sodium, this energy is quantified as 496 kJ/mol, indicating the energy required to ionize one mole of sodium atoms. Understanding this concept is crucial for determining the energy needed to overcome the attractive forces holding the electron to the nucleus.

Photon Energy

The energy of a photon is directly related to its frequency and can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. This relationship is essential for converting the ionization energy of sodium into the corresponding frequency of light required to provide that energy for ionization.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a key component in the equation E = hν, and its value is approximately 6.626 x 10^-34 J·s. Understanding Planck's constant is vital for calculating the minimum frequency of light needed to ionize sodium based on its ionization energy.

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Textbook Question

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv²; 1 electron volt (eV) = 1.602×10^–19 J]

Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.

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Textbook Question

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from -l -1 to l +1 (instead of simply -l to +l). How many orbitals exist in each sublevel? a. s sublevel b. p sublevel c. d sublevel

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Textbook Question

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? a. n = 1 b. n = 2 c. n = 3

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