Question

of the particle represented by the wave packet. Problem 4 In one of the experiments with electrons we follow a beam of electrons as it travels over a distance of 101km. if the size of the initial packet representing the electron is Imm, what is its size at the end of 10'km distance, if the kinetic energy of the electron is (a) 13.6eV, and (b) 100MeV? Hint the relation between the kinetic energy of the electron and its momentum is not always p2 /2m.

Really need help with these two problems ??

Answer 1

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V_g = dw/dK: w = 2 pi v dw = 2 pi dv & K = 2 pi/lambda dK = -2 pi/lamba^2 d lambda V_g = 2 pi dv/- pi/lambda^2 d lambda = -lambda^2 dv/d lambda given that lambda squareroot v^2 - r^2_0 = c = > v^2 - v^2_0 = c^2/lambda^2 2v dv = -2c^2/lambda^3 d lambda dv/d lambda = -c^2/lambda^3 v dv/d lambda = -c^2/lambda^3 squareroot c^2/lambda^2 + v^2_0 = -c^2 lambda/lambda^3 squareroot c^2 + v^2_0 lambda^2 = -c^2/lambda^2 squareroot c^2 + v^2_0 lambda^2 v_g = lambda^2 c^2/lambda^2 squareroot c^2 + r^2_0 lambda^2 v_g = c^2/squareroot c^2 + v^2_0 lambda^2

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