High School

Calculate the average and maximum speed of conduction

electrons in a potassium block (rho_K=856 kg⁄m^3, M=39.1 amu).

Answer :

The average speed of the conduction electrons is related to the RMS speed by the equation: Average speed = √(8/π) x RMS speed.

The maximum speed, we can use the formula: Maximum speed = 2 x RMS speed.

To calculate the average and maximum speed of conduction electrons in a potassium block, we need to consider the density (ρ) and molar mass (M) of potassium. First, we find the number of potassium atoms per unit volume by dividing the density by the molar mass and multiplying by Avogadro's number. Then, we calculate the root mean square (RMS) speed of the potassium atoms using the formula √(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of a potassium atom. The average speed of the conduction electrons is √(8/π) times the RMS speed, while the maximum speed is 2 times the RMS speed.

The average speed of conduction electrons in a potassium block can be calculated using the root mean square (RMS) speed formula, while the maximum speed can be found by doubling the RMS speed. The density and molar mass of potassium are needed to determine the number of potassium atoms per unit volume. It's important to remember that these calculations are based on certain assumptions and formulas, and real-world factors may affect the actual speeds of conduction electrons in a potassium block.

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