Skip to main content
Ch.8 - The Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblem 93
Chapter 8, Problem 93

The binding energy of electrons in a metal is 193 kJ/mol. What is the threshold frequency of the metal?

Verified step by step guidance
1
Understand that the binding energy given is the energy required to remove an electron from the metal surface, which is also known as the work function (\( \phi \)).
Convert the binding energy from kJ/mol to J per electron. Use the conversion factor: 1 kJ = 1000 J and Avogadro's number (\(6.022 \times 10^{23}\) mol\(^{-1}\)).
Use the formula for the work function in terms of frequency: \( \phi = h \nu_0 \), where \( h \) is Planck's constant (\(6.626 \times 10^{-34} \) J·s) and \( \nu_0 \) is the threshold frequency.
Rearrange the formula to solve for the threshold frequency: \( \nu_0 = \frac{\phi}{h} \).
Substitute the converted work function value and Planck's constant into the equation to find the threshold frequency.

Key Concepts

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

Binding Energy

Binding energy refers to the energy required to remove an electron from an atom or a solid, such as a metal. In this context, it is given as 193 kJ/mol, indicating the energy needed to free one mole of electrons from the metal's surface. This concept is crucial for understanding how tightly electrons are held in a material and how this affects their behavior under external influences, such as light.
Recommended video:
Guided course
02:06
Nuclear Binding Energy

Threshold Frequency

Threshold frequency is the minimum frequency of incident light required to eject electrons from a material's surface in the photoelectric effect. It is directly related to the binding energy of the electrons; if the frequency of the incoming light is equal to or greater than the threshold frequency, electrons can be emitted. This concept is essential for linking the energy of photons to the energy required to liberate electrons from a metal.
Recommended video:
Guided course
00:31
Frequency-Wavelength Relationship

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, where photons collide with electrons, transferring energy. Understanding this concept is vital for calculating the threshold frequency, as it illustrates the relationship between light frequency, energy, and electron emission.
Recommended video:
Guided course
02:31
Photoelectric Effect
Related Practice
Textbook Question

The distance from Earth to the sun is 1.5×108 km. Find the number of crests in a light wave of frequency 1.0×1014 s –1 traveling from the sun to Earth.

2153
views
1
rank
Textbook Question

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.

3025
views
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

1155
views
Textbook Question

An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.

1868
views
Textbook Question

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s–1 and the highest frequency of a piccolo is 1.5×104 s–1. Find the difference in wavelength between these two sounds.

2299
views
1
comments