please show all work,thanks!!! a) Calculate the classical electron radius of an

Question

please show all work,thanks!!!

a) Calculate the classical electron radius of an electron by assuming the mass- energy of the electron is due solely to the energy of its electrostatic field. Assume that the electron is a homogeneous solid spherical charge distribution of radius re and relate mass and energy via E mac b) Not worrying about relativity, calculate the velocity of a point on the surface of the electron if your electron is to have a spin angular momentum equal to h/2 (the quantum spin value of the electron).

Explanation / Answer

a :- we know from electrostatic field energy 0f electron

E = [(1/ (4 * pi * apsilon(0))) * e^2] / r(e)   --------> 1

now given E = mc^2                  --------------------->2

from eq 1 and 2 we get

                                                 [ (1/ (4 * pi * apsilon(0))) * e^2 ]/ r(e)   = mc^2

                                                => r(e) = [(1/ (4 * pi * apsilon(0))) * e^2 ] / mc^2 -----------------> (3)

=> e = 1.6 * 10^-16 C , m = 9.1 * 10^-31 kg , c = 3 * 10^8 m/s apsilon(0) = 8.85 * 10^-12 , pi = 3.14

puting these values in expression (3) we get

r(e) = 2.81794032 * 10^-15 m

b :- 1/2 * mv^2 = [(1/ (4 * pi * apsilon(0))) * Z * e^2 ] / r(e)

      mvr = h/2 (given)

=> v = [Z * e^2] / [( pi * apsilon(0)) * h]

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