Question

The density of copper is 8.96 g/cm and its atomic mass is 63.56 g/mol and each Cu atom donates one electron to the conduction electron gas in the metal. If the mean free time is 0.02ps and the mean speed of conduction electron is 1.5×10⁶ m/s, then estimate the drift mobility of electron and the conductivity of copper and also estimate the frequency and amplitude of atomic vibration at

T=300 K.[Nₐ=6.023×10²³
23,k=1.38×10⁻²³ JK⁻¹]

Answer 1

To find the drift velocity of electrons in a copper wire, the density of charge carriers is calculated using the density of copper, atomic mass, and Avogadro's number. With the density of charge carriers, the current, and the cross-sectional area of the wire, the drift velocity can be determined using the formula I = nqAvd.

Step-by-step explanation:

To calculate the drift velocity of electrons in a copper wire, we use the formula I = nqAvd, where I is the current, n is the density of charge carriers (number of free electrons per cubic meter), q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity.

The density of copper is given as 8.80 × 10³ kg/m³, the atomic mass of copper is 63.54 g/mol, and Avogadro's number is 6.02 × 10²³ atoms/mol. Using these values, the density of charge carriers n can be found with the following steps:

1. Convert the atomic mass of copper to kilograms from grams: 63.54 g/mol × 1 kg/1000 g = 6.354 × 10²µ kg/mol.
2. Calculate moles of copper in 1 m³ based on its density: 8.80 × 10³ kg/m³ / 6.354 × 10²µ kg/mol = 1.384 × 10²¸ mol/m³.
3. Calculate the number of free electrons in 1 m³ using Avogadro's number: 1.384 × 10²¸ mol/m³ × 6.02 × 10²³ atoms/mol = 8.34 × 10²¸ free electrons/m³.

With the number of free electrons n, the charge of an electron q = 1.60 × 10²±¹ C, and the cross-sectional area of the wire, the drift velocity vd can be calculated.