(10%) Problem 8: The electric potential near a hydrogen atom can be modeled as t

Question

(10%) Problem 8: The electric potential near a hydrogen atom can be modeled as the equation to the right where ao is the Bohr radius and q is the charge on the central proton V Randomized Variables Otheexpertta.com 33% Part (a) Find an expression for the -component of the electric field, E0 Eo 0 Correct 33% Part (b) Find an expression for the -component (azimuthal) of the electric field. EpCorrect! > 33% Part(c) What is the change in the magnitude of the electric field (in N/C) f a test point moves from the position x = m2a) 0,2-0 to position (x-n'ao, y 0,z-0) Grade Summary Deductions Potential 0% 100%

Explanation / Answer

Part c)

n=5, m=1

V(r) = [(q/40a0)e-2r/a0]*(1+a0/r)

V(r=n2a0) = [(q/40a0)e-2n^2a0/a0]*(1+a0/(n2a0)) = [(q/40a0)e-2n^2]*(1+1/n2)= [(q/40a0)]*e-50*(1+1/25)

V(r=m2a0) = [(q/40a0)e-2m^2a0/a0]*(1+a0/(m2a0)) = [(q/40a0)e-2]*(1+1/m2) = [(q/40a0)]*e-2*(2)

E = -V/r = -{[(q/40a0)]*{[e-50*(1+1/25)]-[e-2*(2)]}}/[(n2-m2)*a0]

Plug values,

n=5, m= 1, q=1.6*10^-19, a0=0.529*10^-10m

E = -{[(1.6*10^-19)/(4*3.14*8.85*10^-12*0.529*10^-10)][[(e^-50)*(1+1/25)]-[(e^-2)*(2)]]}/[(25-1)*0.529*10^-10]

E = 7.36/[(25-1)*0.529*10^-10]

E = 5.8*10^9 N/C

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