Electrical Conductivity of Metals Quiz

Electrical conductivity is inversely proportional to temperature, meaning as temperature increases, conductivity decreases.

σ is defined as σ = (ne²τ) / m, indicating that it is proportional to electron concentration n.

Experimental results show that conductivity is not strictly proportional to electron concentration, contradicting the theory.

<p>The classical free electron theory predicts σ is proportional to $\sqrt{T}$, which is incorrect according to experimental data.</p> Signup and view all the answers

<p>Silver (Ag) has the highest conductivity, measured at 6.30×10⁷ Siemens per meter.</p> Signup and view all the answers

<p>The electron concentration values highlight the diversity in the availability of free electrons, influencing conductivity.</p> Signup and view all the answers

<p>It implies that classical free electron theory fails to fully describe electron behavior in metals, necessitating alternative theories.</p> Signup and view all the answers

<p>Cadmium (Cd) has the lowest conductivity at 0.15×10⁷ Siemens per meter.</p> Signup and view all the answers

<p>Despite zinc having higher electron concentration than aluminum, zinc's conductivity is lower, implying other factors influence conductivity.</p> Signup and view all the answers

<p>Fermi energy represents the most probable or average energy of electrons during energy transitions at temperatures above absolute zero.</p> Signup and view all the answers

<p>N(E) is defined as the product of the Fermi factor, f(E), and the density of available energy levels, g(E), across a defined range of energy.</p> Signup and view all the answers

<p>The total electron density, n, is evaluated by integrating N(E) from E=0 to E=Emax, which corresponds to the maximum energy of the electrons.</p> Signup and view all the answers

<p>At T=0K, the Fermi factor f(E) is 1, and Emax equals EF; therefore, the electron density is directly associated with the density of states at Fermi energy.</p> Signup and view all the answers

<p>The integral expression for n signifies the total number of electrons per unit volume calculated from the density of states up to the Fermi energy level.</p> Signup and view all the answers

<p>The connection is provided by the expression: $g(E)dE = (\frac{3}{8\sqrt{2}\pi m^2})\sqrt{E}dE$.</p> Signup and view all the answers

<p>Fermi energy determines the highest energy level occupied by electrons at absolute zero, influencing their distribution and available states at higher temperatures.</p> Signup and view all the answers

<p>The Fermi factor, f(E), provides the statistical occupancy of energy states, dictating how many electrons occupy a given level at specific temperatures.</p> Signup and view all the answers

<p>The integration process accumulates the contributions of all energy states up to a maximum energy, providing a total count of electron density in the material.</p> Signup and view all the answers

<p>As temperature increases, the Fermi energy remains relatively constant, but the distribution of occupied energy states shifts, allowing more electrons to have energies above the Fermi level.</p> Signup and view all the answers

<p>The main limitations include the inability to explain certain conductivity phenomena and the failure to account for quantum effects such as electron energy quantization.</p> Signup and view all the answers

<p>Fermi energy is the highest energy level occupied by electrons at absolute zero temperature, and it helps in understanding the distribution and behavior of electrons in metals.</p> Signup and view all the answers

<p>Quantum free electron theory incorporates the principles of quantum mechanics, allowing for accurate predictions of electron behaviors and energy distributions, unlike classical theory.</p> Signup and view all the answers

<p>The Fermi factor describes the probability of occupancy of electronic states and depends on energy and temperature, decreasing as energy increases above the Fermi level at higher temperatures.</p> Signup and view all the answers

<p>Phonon vibrations contribute to scattering events that affect the movement of free electrons, thereby influencing electrical conductivity.</p> Signup and view all the answers

<p>The effective mass is a modified mass that accounts for the interaction between electrons and the periodic potential of the lattice, impacting the calculation of conductivity.</p> Signup and view all the answers

<p>It assumes that all collisions between free electrons and positive ion cores are elastic, meaning there is no loss of energy during these interactions.</p> Signup and view all the answers

<p>The formula is $E_F = kT_F$.</p> Signup and view all the answers

<p>The Fermi factor is the probability of occupation of a given energy state at a specified temperature in thermal equilibrium.</p> Signup and view all the answers

<p>When $E &lt; E_F$ at $T = 0$, the Fermi factor $f(E)$ equals 1, meaning those energy levels are completely occupied.</p> Signup and view all the answers

<p>For $E &gt; E_F$ at $T = 0$, the Fermi factor $f(E)$ equals 0, indicating these energy levels are completely empty.</p> Signup and view all the answers

<p>As temperature increases, the Fermi factor remains 1 for $E &lt; E_F$, indicating these levels remain fully occupied.</p> Signup and view all the answers

<p>The Fermi factor for $E &gt; E_F$ decreases rapidly to 0 as temperature increases, meaning those levels are less likely to be occupied.</p> Signup and view all the answers

<p>As temperature increases, electrons near the Fermi level shift to higher energy levels, which can be empty at 0 K.</p> Signup and view all the answers

<p>The relationship is defined by the equation $T_F = \frac{E_F}{k}$.</p> Signup and view all the answers

<p>A value of 1 indicates full occupation of an energy level, while a value of 0 indicates complete emptiness.</p> Signup and view all the answers

<p>The Fermi distribution affects electrical conductivity and heat capacity, influencing how materials respond to temperature changes.</p> Signup and view all the answers

<p>According to QFET, the specific heat at constant volume (Cv) is expressed as $C_v = \frac{2k}{E_F} R T$, indicating its dependence on the Fermi energy (EF).</p> Signup and view all the answers

<p>QFET suggests that electrical conductivity (σ) is inversely proportional to temperature (T), expressed as $\sigma \propto \frac{1}{T}$.</p> Signup and view all the answers

<p>Electrical conductivity (σ) is calculated as $\sigma = \frac{n e^2 \lambda}{m^* v_F}$, showing that σ depends on both electron concentration (n) and Fermi velocity ($v_F$).</p> Signup and view all the answers

<p>The specific heat constant (Cv) calculated using QFET is approximately $10^{-4} R T$, which is in excellent agreement with experimental values.</p> Signup and view all the answers

<p>The atomic weight and density of sodium are crucial for calculating its Fermi energy, allowing us to quantify the energy levels of free electrons in the metal.</p> Signup and view all the answers

A theory explaining electrical conductivity in metals by assuming free electrons move like gas molecules and obey classical physics.

A collection of negatively charged particles in a metal, not bound to any specific atom, responsible for electrical conductivity.

A physical model describing the behavior of electrons in a metal, assuming they move freely and collide with positive ions and other electrons.

Vibrations of atoms in a material's lattice structure that can transfer energy and influence electrical conductivity.

The average energy of an electron due to thermal motion at a given temperature. It determines how easily electrons can contribute to conductivity.

The average velocity of free electrons in a metal due to thermal motion. It influences how quickly electrons can move and conduct electricity.

The ability of a material to conduct electric current, quantified by the ease with which electrons can move under an electric field.

The relationship between the temperature and electrical conductivity of a metal based on experimental observations.

The classic free electron theory's prediction of how electrical conductivity changes with temperature in metals.

Describes the disagreement between the classical free electron theory and experimentally observed behavior regarding the temperature dependence of electrical conductivity in metals.

The relationship between the number of free electrons per unit volume (electron concentration) and electrical conductivity as predicted by the classical free electron theory.

The actual relationship between conductivity and electron concentration observed in real metals.

The observation that conductivity is not directly proportional to electron concentration in real metals, contradicting the prediction of the classical free electron theory.

The ratio of the number of free electrons to the total number of atoms in a material, indicating how many electrons can contribute to electrical conductivity.

A measure of how easily an electric current can flow through a material, with higher conductivity indicating better flow.

The specific heat capacity of a metal at constant volume, determined by the relationship between heat absorbed and temperature change. It's often a small value due to the limited degrees of freedom for electrons at low temperatures.

A theory explaining the behavior of electrons in metals by incorporating quantum mechanics, specifically Pauli exclusion principle and Fermi-Dirac statistics.

The energy level at which the probability of finding an electron is 50% at absolute zero. It's a key concept in understanding the thermal properties of metals.

The concentration of free electrons in a material. Higher electron concentration generally leads to higher electrical conductivity.

The temperature at which the Fermi energy is equal to the average thermal energy of the electrons.

A mathematical expression describing the probability of an energy state being occupied by an electron at a given temperature.

The product of the Fermi temperature and Boltzmann constant, which is equal to the Fermi energy.

At absolute zero (0 Kelvin), all energy levels below the Fermi energy are completely filled, while all energy levels above it are empty.

At ordinary temperatures, the probability of occupying an energy level below the Fermi energy is still close to 1, while it falls rapidly to zero for energy levels above the Fermi level.

The number of available energy states per unit energy range in a material. It determines how many electrons can occupy different energy levels.

The product of the Fermi factor and the density of states, representing the number of electrons per unit energy range.

As the temperature rises, electrons near the Fermi level gain thermal energy and can transition to higher energy states that were initially empty.

The number of free electrons per unit volume in a material. It influences how well a material conducts electricity.

Boltzmann constant is a fundamental constant describing the relationship between temperature and energy.

The relationship between electron density and Fermi energy at absolute zero temperature (0 K). At this temperature, all energy levels below EF are filled, and all levels above are empty.

A model explaining the behavior of electrons in a material, assuming they move freely and obey quantum mechanics.

The maximum energy that an electron can possess in a material at absolute zero temperature. It's the same as the Fermi energy at 0 K.

In the context of the Fermi factor, it refers to the energy of a specific energy state

The condition where all energy levels below EF are filled with electrons and all energy levels above EF are empty. This occurs at absolute zero temperature (0 K).

The total number of electrons in a material can be calculated by integrating the product of electron density of states and the Fermi factor from zero energy to the maximum energy.

The electron density can be calculated by integrating the electron density of states over a specific energy range.