Question

Atoms are found to move from one lattice position to another at the rate of 300,000 jumps/s at 500 0C when the activation energy for their movement is 10,000 cal/mol. Calculate the jump rate at 400 0C.

Answer 1

The jump rate at 400 0C is approximately 100,829 jumps/s.

Step-by-step explanation:

To calculate the jump rate at 400 0C, we can use the Arrhenius equation:

k = Ae^(-Ea/RT)

Where k is the jump rate, A is the frequency factor, Ea is the activation energy, R is the ideal gas constant, and T is the temperature in Kelvin.

Given that the jump rate at 500 0C is 300,000 jumps/s and the activation energy is 10,000 cal/mol, we can plug in these values:

300,000 = A * e^(-10000/ (8.314 * 500))

Solving for A:

A = 300000 / e^(-10000/4157)

Now we can use this value of A to calculate the jump rate at 400 0C:

k = A * e^(-10000/ (8.314 * 400))

Calculating:

k = (300000 / e^(-10000/4157)) * e^(-10000/3325)

k ≈ 100,829 jumps/s