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Ch.7 - Quantum-Mechanical Model of the Atom
Chapter 7, Problem 79

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?

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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 required to remove an electron from an atom in its gaseous state. For hydrogen, this energy is specifically the energy needed to remove the single electron from its ground state, which is approximately 1312 kJ/mol. Understanding this concept is crucial for calculating the energy needed for ionization and for determining the corresponding wavelength of light.
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Ionization Energy

Photon Energy and Wavelength

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. To ionize a hydrogen atom, the energy of a photon must equal or exceed the ionization energy. This relationship allows us to calculate the wavelength of light that can provide sufficient energy for ionization.
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Ground State of Hydrogen

The ground state of hydrogen refers to the lowest energy level of the hydrogen atom, where the electron is closest to the nucleus. In this state, the electron is in the 1s orbital, and any energy input must be sufficient to overcome the attractive force between the electron and the nucleus to achieve ionization. Understanding the ground state is essential for determining the specific energy requirements for ionization.
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Related Practice
Open Question
A green leaf has a surface area of 2.50 cm². If solar radiation is 1000 W/m², how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.
Open Question
In a technique used for surface analysis called Auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons—called Auger electrons—from the metal surface. The kinetic energy of the Auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in Auger electrons with a kinetic energy of approximately 506 eV. What is the de Broglie wavelength of one of these electrons? [KE = 1/2mv^2; 1 electron volt (eV) = 1.602 * 10^(-19) J]
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]

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Textbook Question

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

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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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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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